It's hard to create a story where both sides are fully sympathetic and yet in a real conflict with each other. But sometimes the authors manage to pull it off.
This is not when the characters on both sides are somewhat sympathetic, merely believe in their own actions without being fully sympathetic, or are in a temporary conflict by mistake. No, this is when both sides are unambiguously Good AND locked in a real conflict with each other.
This can be a philosophical struggle where Lawful Good and For Great Justice stand against the forces of Chaotic Good and For Happiness. In this case, the conflict is between a Hero Protagonist and a Hero Antagonist. It can also be when unambiguously good characters find themselves on different sides of a Grey and Grey Morality conflict. In either case, they are often reluctant to fight each other but can have a hard time understanding each other's point.
This trope is closely related to White and Grey Morality, but when that trope is played completely straight there can be no conflict beyond mere misunderstandings.
Compare with Both Sides Have a Point, Your Terrorists Are Our Freedom Fighters and Utopia Justifies the Means. Contrast to Black and White Morality and Evil Versus Evil. Unless the two sides ultimately reconcile, almost certain to end in a Downer Ending — and because they are both fighting for good ends, it can be very hard for them to reconcile, owing to what they must sacrifice.
Examples
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Anime
X/1999 might to some degree be seen this way. The goals of both groups are reasonable. Saving the Earth from human destruction or saving humanity from extinction.
However, most of the Dragons of Earth could care less about saving the Earth.
Most arcs of Mahou Sensei Negima! end up being this in some form or another, as almost every antagonist turns out to have a rather justifiably heroic motivation, although their methods are usually uncomfortably pragmatic. The exception is Tsukuyomi, who's just nuts and horny.
Cat's Eye is a story about eponymous trio of art thieves and their antagonists from police. The cops are unambigously heroic, while the thieves have good intentions, and frequently act geniunely heroic, for example, they once rescued children from burning house, and also, they saved the detectives from really evil criminals a few times.
In Suzumiya Haruhi, it is stated that the Organization, Koizumi's faction, and the time travelers, Mikuru's faction, are fiercely against each other. However, both sides are just out to maintain the status quo, and protect the titular character. Meanwhile, Yuki's faction are formless data entities, with their own inner power struggles and wars. On the whole, they prefer to maintain the status quo by not interfering except to maintain the masquerade, while trying to learn how Haruhi's powers work. As for the three agents, they have stated that should their factions go to war, they will stand by the SOS Brigade, breaking ties if they have to.
Good guys duel each other all the time in Yu Gi Oh, but the struggle of Team 5D's versus Team Ragnarok really stands out. They may be dueling in a tournament match, but it's a full-on conflict of genuinely good-hearted heroes chosen by their respective gods to destroy the evil antagonists in the next round. Each side believes the other fights for good, but is also unworthy and incapable of defeating the Lords of Yliaster.
Since Hikaru no Go is about characters playing a board game, it's easy to find situations were the main character is playing against a fully sympathetic character. The conflict is serious since the characters are (or are trying to be) professional players and consider Go to be their main occupation in life. This is very apparent during the pro exams where Hikaru has to play against his friends Waya and Isumi who had helped him a lot in preparing for the pro exams. Only a very limited number of people can pass the exams, and every loss endangers their chances.
While Dog Days does have evil creatures, the story is generally about the Good Guys fighting a war with other Good Guys, where "war" means Playground Olympics.
There are demons however the only one seen was possessed by a sword though there is stuff going on...offscreen.
In C Control, according to Masakaki's superior, everyone involved in the Financial District was a good guy who was trying to make the world a better place, and the conflict was fought between heroes with different plans and methodologies for doing so.
Comic Books
The Civil War crossover in the Marvel Universe, where superheroes fought each other over a Super Registration Act. (At least, this trope was the intention - there's a lot of Depending on the Writer involved as to "who's right" and if/how much the other side gets demonized. When all was said and done, fans concluded that the pro-registration heroes crossed a few too many lines to be considered the "good guys".)
The X-Men vs Avengers crossover back in the 80's, where the two teams were fighting over the fate of Magneto, who at the time had reformed and joined the X-Men. The Avengers—who generally turn a blind eye to the X-Men's actions since they know the mutants are heroes—wanted to bring a known terrorist to justice, while the X-Men wanted to protect their ally.
It happened again in 2012 (as Avengers Vs X-Men this time); now over Hope Summers, who was expected to become the next host of the Phoenix Force. The X-Men again want to protect one of their own, while the Avengers see the Phoenix as a potential threat (not without cause, mind you). However, this premise was discarded once the Phoenix actually arrived, as the handful of X-Men that the Phoenix took as hosts (since Hope was incapacitated) started Jumping Off the Slippery Slope, with even Cyclops eventually becoming a Knight Templar. (The Avengers aren't completely innocent either, but like in Civil War they're still Designated Heroes at the very least.)
Just prior to the latter scrap with the Avengers, the X-Men (mainly Cyclops and Wolverine) fought amongst themselves in Schism over whether or not the younger members should be involved when the group faces life-or-death battles.
Wonder Woman gets this a lot, since she explicitly has no code against killing, and this occasionally brings her into conflict with Superman and Batman. A prime example is the graphic novel The Hiketeia, in which Batman is the primary antagonist.
The inter-company crossover JLA-Avengers featured the two teams pitted against each other to collect various powerful artifacts from each universe. The resulting competition results in several fights between members of the groups, including a long awaited battle between Superman and Thor Superman wins, but is so weakened from the battle that the rest of the Avengers manage to take him down.
Fan Work
The Magical Girl Lyrical Nanoha fanfic Game Theory continues this trend from the show with Nanoha and Fate against the TSAB. Both sides are sympathetic and happen to have mutually exclusive goals, although the former are being manipulated by Precia.
In Rolling in Beaches, the hippocampi/Scaly Back River Clan conflict is best described as this, as neither side is evil; however, a major misunderstanding on the dragons' side, and a bit of Fantastic Racism on the sea ponies' part, has them at each other's throats. Luna also suspects that Erebos was manipulating events.
Fate Stay Night Ultimate Master has Ben Tennyson taking part in the Holy Grail War. Since the Holy Grail War follow the There Can Be Only One system, he inevitably ends up clashing with Fate/Stay Night protagonists Shirou and Rin, despite their goals being the same (prevent the Holy Grail from falling into the wrong hand). Later chapters, however, suggest this will change.
Film
In probably the only true manifestation of this trope, the two main characters from The Iron Monkey are both doctors and expert martial artists. It's no surprise that they end up fighting side-by-side at the end, but for most of the movie, one is motivated by fighting the corrupt government, while the other is motivated by preventing said corrupt government from holding his son hostage by catching the other one. Neither side has the moral high ground.
The T-800 versus the police in Terminator 2: Judgment Day. Arnie wants to ensure the destruction of Cyberdyne, whereas the police merely do their job, stopping an apparent terrorist act.
Unfortunately a big downer in The Matrix. Neo and his allies frequently kill/injure law enforcement agents, who are simply not aware being part of the Matrix. They are also extremely ruthless about it; in the first movie especially they don't so much fight law enforcement officers as massacre them, particularly in the Hallway scene (Neo even machine guns a guard who was reading a newspaper). Morpheus gives their stone cold philosophy on the subject early on- everyone they are trying to save is plugged into the systemnote For instance, they could at any moment be possessed by an Agent, and Agents can actually see and hear what they see and hear, and "that makes them our enemy". It's actually quite chilling when you consider the implications of that, since in theory they are willing to kill even civilians to achieve their end. In the sequel, in fact, they do just that, when they blow up a power station and kill everyone who stands in their way, or beat them up and leave them to die
In The Fugitive, there's US Marshal Sam Gerard, whose job is to capture murder suspect Richard Kimble. Richard Kimble is innocent however, and his job is to find the real murderer and clear his own name.
Warrior. Both brothers have equally compelling reasons for wanting to win the MMA championship, one to keep his family home from foreclosing and the other to honor his fallen war buddy by taking care of his friends family.
Literature
In A Dark Wood by Michael Cadnum, a retelling of Robin Hood from the perspective of The Sheriff of Nottingham, a good man who distastefully upholds brutal laws, yet is eventually able to recognize that his outlaw adversary is also a good man.
Yeoman and Popinjay hate each other in the Wild Cards books, specifically because Yeoman is a mass murderer (of evil people) while Popinjay is a private detective who nevertheless views such things as monstrous.
Honor Harrington, between the fall of the Committee and the Battle of Manticore (imagine the United States and the United Kingdom locked in a total war). It eventually gets really frustrating (and Tear Jerking) to watch good, sympathetic characters killing each other (especially Javier Giscard's death, defending a vital industrial node from Honor's raids).
Les Misérables: Valjean and Javert. One is a guy trying to atone for his past sins by showering kindness and mercy on everyone who crosses his path, occasionally risking even his life to do so. The other is a policeman trying to recapture a convicted thief and parole violator who escaped from prison.
The majority of the Kings featured in A Song of Ice and Fire, and the accompanying Game of Thrones TV adaptation, are a murky shade of good at worst. Renly, Robb Stark, and to a lesser extent Stannis are all portrayed as this.
Live-Action TV
Buffy and her initial clash with the soldiers of the Initiative - especially Riley - is like this. It gets gray and grayer once we learn more about project 314 and Maggie Walsh's plans though.
Her initial run in with Sid the puppet Demon Hunter was the result of a misunderstanding (her power made him think she was a demon, and the evil puppet thing is too much a cliche for her to think it was anything else).
Angel The fight between Angel and Spike in the Season Five episode 'Destiny'. Both have a soul, both want to drink from the cup of perpetual torment - whoopsie, someone got staked.
In the second season of The X-Files we finally learn that Skinner is not as cold-blooded and ignorant as he appeared to be at the end of the first season, but that he is merely forced by the CSM/the Man to give Mulder a hard time.
Supernatural addresses this in the second season arc involving Gordon Walker. He is a hunter, a relentless one, but only interested in killing vampires/demons - at first. However he crosses over into Grey or Black Morality, when he doesn't relent from trying to kill a group of vampires who have abstained from feeding and are trying to just live their lives, and it is also implied he kills supernatural creaturs solely out of hate for turning his sister and ruining his life.
The re-imagined Battlestar Galactica has the conflict(s) between Commander Adama and President Roslin, Starbuck vs. Kat, Starbuck vs. Apollo, Everyone vs. Helo - and a lot more. Most of them take place between two parties who want the best for the fleet.
For the first half of Person of Interest's first season, the two sides were John Reese and Harold Finch, vigilantes stopping violent crimes before they happened, and NYPD Detective Carter, their Sympathetic Inspector Antagonist. Then when Reese is shot by his former associates in the CIA, Carter joins up with him and Finch because she wanted to catch them, not kill them.
In the Star Trek: Voyager episode "Timeless", Harry Kim is trying to alter the timeline to make sure Voyager wouldn't crash, while Captain LaForge is trying to stop him, partly to protect his own crew, and partly because messing with Time Travel does not tend to end well in the Star Trek Universe.
Professional Wrestling
Good vs good is something that is fairly uncommon for the simple reason that when you have two good guys who are equally popular, the crowd is divided between them. This generally makes bad TV, so it is avoided if possible. If you have two faces, generally one guy turns heel, at least for the duration of the feud.
The Ultimate Warrior vs Hulk Hogan, culminating at Wrestlemania 6 in a title-against-title match.
The Rock vs Hulk Hogan, although in a special case, Hulk's popularity was so great that the Rock turned heel mid-match, only to turn back afterwards.
Hulk Hogan was actually a Heel in that match as a member of the nWo. He didn't turn face until after the match when he shook The Rock's hand and both fought off Kevin Nash and Scott Hall.
TNA recently had Ken Anderson, Jeff Hardy and Kurt Angle go into a three way for the TNA Heavyweight title; all were faces, but Jeff Hardy turned heel at the conclusion with the reveal of the Immortal.
Though they were in Texas at the time, so Rock was the Designated Villain for the match, even after Austin turned. It wasn't until the next night that he built any real heat as a heel.
The Rock still wasn't the "villain" per se; the crowd just didn't cheer for him, at least not at first. The match is actually a good example of why this trope is so rare, since the fans didn't seem to know how to react to the Rock, since against anyone else, or in any other state, they would be cheering for him too. Also, near the end of the match when it was clear what side Austin was on, the crowd did start cheering on The Rock, and gave him a massive ovation the last time he kicked out of Austin's savage beating.
Wrestlemania XII was unique in Wrestlemania history in that the two wrestlers who faced each other for the title in the main event were not feuding, were not presented as having any sort of bad blood, and in fact got along with each other extremely well, both openly declaring on a number of occasions that they enjoy working with each other and look forward to the challenge. It wasn't even like Hogan vs. Warrior where the script went out of its way to present neither of the enemies as being fully in the right or being arrogant: they weren't enemies. There was no feud at all and no moral high ground to be seen. Rowdy Roddy Piper even used his in-ring charisma at one point to influence the crowd into not booing previous Heel Michaels. They did everything they could to show that we're not necessarily supposed to be rooting for either man, and instead focused on selling the main event based on its own merits: an hour-long "iron man" match which ended up GOING INTO OVERTIME!.
Also counts as Hilarious in Hindsight The two "not enemies"? Bret Hart and Shawn Michaels, who developed real heat with each other after this match due to the winner's instance that the loser get out of the ring so he could celebrate his win. After that, the two had massive animosity towards each other that burnt for over a decade before they sussed it out.
Tabletop Games
When a non-evil party goes up against non-fallen celestials in Dungeons & Dragons, it's this trope.
Discussed in Champions of Valor. To paraphrase the author, good-on-good violence is unlikely to occur in FR since good-aligned characters and nations are likely to have bigger fish to fry.
In Talisman, characters of the "Good" alignment are supposed to fight each other just like everyone else, and in the endgame they HAVE to fight each other.
Video Games
Applies to every Fighting-game. The results and causes may vary, but at one point or the other, 'Good characters' will battle 'Good characters'.
The Soul Calibur series. With the exception of three or four characters, they're mostly heroes who will battle whoever it takes to obtain Soul Edge.
It's more complicated that than that. There are straight examples, such as in III Ivy fighting Sigfried (with a unique pre battle story), as both characters only seek the destruction of the sword but for different reasons and in different ways. Ivy believed the destruction of both swords would be the end of the conflict, but Sigfried wanted to use Calibur to destroy Edge. Depending on the fight it, can be any shade of conflict there, from Tali's white to Maxi's grey to Nightmare's black.
Very, very common in the Tales Series, although the good side not controlled by the player is generally more "ends justify the means" and willing to employ genuine evil in their pursuit of noble goals.
Spire also fits this category, since he's hoping to revive/find out more about his species.
The conflict between Thorndyke and the Nereids in Soul Nomad qualifies. Thorndyke wants Feinne undisturbed to prevent the situation from potentially getting much worse. The Nereids want to kill Feinne to solve the crisis of the World Eaters.
Ar Tonelico 2. Where to begin?! While people do truly horrifying things to each other, not a single faction is doing it out of selfish interest. Each one believes that they are doing the right thing for the world and the people who live in it, and each of them have their points. Even the Mad ScientistBig BadInfel only wish to stop the suffering of the people by Brain Uploading every single soul into Instrumentality, and she does this out of a sense of responsibility for failing to provide a paradise on earth long, long time ago.
Related to Color-Coded Multiplayer many games with multiplayer options only let you play as the good guys or Palette swaps of the main protagonist.
The original Halo's multiplayer consists of Spartans (who are on the same side in the game's story). The sequel adds the enemy Elite aliens, but only after they had done a Heel Race Turn.
Touhou games have never had any true villains. Just a lot of spoiled, lonely, stir-crazy, lazy, playful and/or protective characters. The only real life-threatening situation in a long time has been the last stage of Subterranean Animism where defeat would have cause the protagonist to fall into the Hell of Blazing Fires, which only because the final boss (Utsuho Reiuji) went temporarily crazy. The only character stated to be evil (Seiga) wasn't actually up to anything when she was fought.
Played fairly straight in the first Advance Wars game. The vast majority of the Commanding Officers are all morally upright people who are convinced that they're fighting for justice. This does not stop them from getting in drawn out territorial conflicts throughout most of the campaign.
The battle on the Fugue Plane in Neverwinter Nights 2 features celestials versus paladins, and potentially paladin versus paladin.
In Pokemon Black And White this is the case with N (a Friend to All Living Things who wants to free Pokemon from humans) and the player character, to the point where they are both recognised as heroes by Zekrom and Reshiram.
Metaphysically, the introduction to Ultima IV has you doing this, having to pick between eight perfectly moral and virtuous options in a series of hypothetical moral dilemmas in order to choose a starting class (assuming you answer truthfully instead of just picking the virtue that corresponds to the class you want to play).
Dissidia: Final Fantasy has the heroes fighting each other (either to test themselves or to settle points of conduct) just as often as they fight the villains.
In Dragon Age: Origins, the Warden can end up fighting Ser Cauthrien twice, though on both occasions it can be avoided with the right dialogue choices and high persuasion. The Warden is the commander of the forces battling the Darkspawn, and Cauthrien is an unambiguously heroic and honorable knight who just happens to be in the service of the main human antagonist, the usurper Teyrn Loghain.
Apollo Justice gives us Apollo versus Klavier. Both have dedicated their lives to uncovering the truths in the cases their involved in, but just happen to be on opposite sides of the court as a defense attorney and prosecutor. The two occasionally even share information or help each other out in the interest of finding the true guilty party, including when Klavier's own bandmate and, later, brother are on the stand.
Mario vs. Donkey Kong. The antagonist Donkey Kong is by no means evil; the only reason players are pitted against him is that he steals the toys from Mario's factory, which Donkey falls in love with, and Mario is trying to take them back.
In StarCraft II, should you choose to protect the colony, you wind up having Jim Raynor pitted against the Protoss Salendis.
Western Animation
The conflict between Daria and Tom in the seasons 4-5. Agree with the creator of the series, neither of them is malicious, not even touching to be evil. And, agree with some fans, Daria misinterpreted the things in Tom, and well, took them both to have conflicts that later was resolved in a manner not very expected, but not a Downer Ending.
Though the occasional implication that she's developing an Ambiguous Disorder blurs things
Ben 10: Ultimate Alien's finale focus around the return of an Eldritch Abomination named Diagon, leading to its Arch-Enemy Sir George to come back from retirement. However, Diagon didn't show up until the finale, and George turned out to have some Knight Templar tendencies, so the episodes building up to this finale partially focused on Ben and his team fighting with Sir George and his Forever Knight over the way to deal with Diagon (as well as the anti-alien persecutions caused by George).
Other
This trope is demonstrative in a lot of forum games where players may be in charge of a fictional faction or nation, there will be a few players who, (if they do not merely make their faction/characters a frontpiece for their socio-political views) try to make them as lawful good as possible with regards to their in-game culture so that roleplay wise most good people in the game world would see that faction as mostly good on top of the faction seeing itself as good. Of course this does not mean that the liberal paradise republic that legalizes prostitution is going to get along well with the highly religious absolute monarchy next door that abhors slavery and has strict privacy and civil rights laws and it is not uncommon that this trope will soon occur for one reason or another.
