Mentors are always helpful to any self respecting hero. Not only can they pass on knowledge or training, but also points of view, philosophies and even allies (or possibly enemies...). Unfortunately, sometimes The Hero is particularly talented (or maybe in the right place at the right time) and has more than one mentor trying to recruit them as a student...and they almost always have opposing philosophies.
Opposed Mentors are an excellent opportunity for character development; the hero is given a choice between them, and the one he chooses (and whether he comes to regret it eventually) can represent what the hero is on the path to becoming (or risks becoming). Expect the mentors to alternately argue with each other by proxy as they give the hero advice (Bonus Points for having the hero "trapped" between them as they shout back and forth, eventually ignoring the hero all together in favour of their opinion). If one of the mentors is evil you can almost guarantee that they were once a student of the other mentor and if not, that both mentors were students of the same master (who the evil mentor no doubt betrayed, although a good mentor being a Defector from Decadence isn't unheard of).
It's also just as likely that both mentors are good but disagree on some key point. In this case it's far more likely that the hero will either remain neutral and learn from both of them or that one of them will die or turn evil. Sometimes one of the mentors is proved to be right (in which case the other mentor is likely to accept that and mend their ways or, as you might guess, turn evil). Other times the hero will, through accepting both their philosophies, surpass them both (generally by becoming a Jack of All Stats).
If the hero rejects a mentor then the spurned mentor will almost certainly take on The Rival as a student (possibly tempting them towards evil) or stick around until the hero discovers that their chosen mentor wasn't all they appeared to be.
Ways mentors can be opposed include, but are by no means limited to: training regimes (Wax On, Wax Off versus Training from Hell), ethics (With Great Power verses Might Makes Right), choice of techniques (Magic Versus Science or Fighter, Mage, Thief can both be a source of duality), whether talent matters (Hard Work Hardly Works and The Gift versus Training from Hell) and progress (the new ways versus the Good Old Ways). See also Dueling Messiahs, who are more concerned with doing right by the world than just one person.
Musashi's great rival Sasaki Kojiro also has opposed mentors. First is his adopted father Jisai, who frantically tries to keep Kojiro away from the dangerous life of a swordsman, (despite being a skilled Old Master himself) and then there's the half crazy Blood Knight Ito Ittosai, who knows only too well how to bring out Kojiro's inner Blood Knight.
A Bronx Tale is about a kid called Calogero growing up under the conflicting influences of his hard-working, honest, but poor father, and the charismatic, rich and powerful, Affably Evil local mafia don Sonny.
Star Wars - Anakin Skywalker has to choose between following Obi wan Kenobi and Palpatine. Eventually, he chooses Palpatine and turns to the Dark Side.
I ♥ Huckabees featured philosophically opposed existential detectives (who both served as Trickster Mentors for their clients) who may or may not have actually been working together, but would never admit it.
Platoon: Wide-Eyed Idealist Chris is torn between two Sergeants about how he should conduct himself in Vietnam. As his closing monologue goes" The war is over for me now, but it will always be there, the rest of my days. As I'm sure Elias will be, fighting with Barnes for what Rhah called "possession of my soul".
The Forbidden Kingdom had Jackie Chan and Jet Li as the two mentors. It even provides a quote, "Two tigers can't rule the same mountain."
In the Warrior Cats novel Crookedstar's Promise, the titular character is taught by his real mentor, Cedarpelt, but, unknown to other cats, he also is trained in his dreams by the deceased warrior Mapleshade. Mapleshade focuses more on combat skills, while Cedarpelt tries to explain that being a warrior is about more than just being a good fighter. Even their advice on battle moves differs, though that can be explained by the fact that Mapleshade came from another Clan.
In Life of Pi the title character has two mentors, both named Mr. Kumar: the first is an uneducated but devout Muslim shopkeeper while the other is Pi's intelligent, atheistic science teacher. Despite their antithetical worldviews they actually get along well the one time they happen to meet each other, and Pi, whose two main interests are religion and animals, doesn't seem to feel conflicted between them.
In Atlas Shrugged, science professor Robert Stadler and philosophy professor Hugh Akston competed for college students John Galt, Ragnar Danneskjold, and Francisco d'Anconia. The latter won and later joined their movement, while the former went on to become a government sell-out.
In Good Omens, Heaven and Hell both send hand-picked childhood influences (a nanny, a gardener, two teachers) to the home of the boy they think is The Antichrist. It's the wrong boy.
Live Action Television
In ScrubsDr. Kelso and Dr. Cox have this dynamic for the first few episodes, with both being presented as possible mentors to JD. With Dr. Kelso being concerned with money (arguing that if the hospital doesn't make a profit, it'll close) and Dr. Cox arguing that the patient should come first. JD chooses Cox, earning him Kelso's contempt (although later episodes show Kelso in a better light). They recycled this plot a few times;
One episode had JD think that Cox and a Private Practice Doctor were warring mentors to him, but really it was about the PPD having slept with Jordan.
When JD moved up to attending in the middle of the series they replayed the Cox vs Kelso only this time with Cox taking Kelso's part and JD taking Cox's part with some of the new interns being the ones caught in the middle.
In the last season, after the Retool Drew was subject to the warring between Denise and Cox (although given he was in a relationship with Denise it was as much about the sexual relationship as much as the mentorship).
Xena: Warrior Princess: In Xena's backstory the evil shamaness Alti is pitted against Cyane, the noble Queen of the Amazons. They even have a mental struggle with Xena literally between them. Cyane wins, but Xena chooses Alti, and kills Cyane and the other leaders of the northern Amazons, helping Alti to trap their souls and prevent them from crossing over. Xena eventually sets things right. Alti is also pitted against Lao Ma, though they never directly argue over Xena.
Alti: "Your friend you told me about, Lao Ma, her powers come from denial, from self-sacrifice, from the light. That’s not for people like you and me. I wanna tap into the heart of darkness - the sheer, naked will behind all craving, hatred, and violence. I’ll become the face of death itself - capable of destroying not only a person’s body, but their soul. Help me, and I’ll make you ‘Destroyer of Nations’.”
An episode of Parks and Recreation sees Ron and Chris clash over the best way to train April to be a manager. They get competitive, and have a wager over whose method can get the most productivity out of Jerry in the course of a workday. In the end, they discover that April set the two of them against each other so she could blow off the management training, and see this as a sign that she's going to be fine on her own.
In The Elder Scrolls V: Skyrim you have the choice of being backed by the Greybeards (who are Actual Pacifists) and the Blades (who want to slay every single dragon in existence). In the end The Blades ask you to kill the dragon who served as the mentor to the Greybeards, forcing you to choose one side or the other. Neither side is shown as better or worse than the other.
In Grand Theft Auto V: Michael and Trevor to Franklin. One is corrupt but level-headed, the other is honourable but excessively violent. Both of them butt heads trying to teach Franklin the ropes of high-class heists and their rivalry obstructs them to the point that Franklin has to choose which one to kill, or if he's willing to risk his life and millions of dollars to save them both.
In Avatar: The Last Airbender , Katara and Toph have very different opinions on how Aang should be trained. Katara, his waterbending teacher goes for the soft, encouraging, positive attitude, while Toph, his earthbending teacher, prefers the rougher, blunter, drill sergeant style. This culminates in an interesting mud-fight scene between the two.
Zuko also had the dueling influences of his father, a power-mad warlord attempting to raise his son to follow in his footsteps (or get him killed so his sister could do so, whatever) and his uncle, a wise Atoner/Defector from Decadence who wanted his nephew to pursue peace on taking the throne.
American Dad! played with this. Stan and Francine wanted to raise Steve different ways, and Steve ended up with a clone, allowing both parents to try their own ways. It turned out neither one alone worked.
In a gag on The Simpsons Lisa makes a square on a family heirloom patchwork quilt honoring her two musical mentors:
Look Mom, I've finished my patch. It depicts the two greatest musical influences in my life. On the left is Mr. Largo, my music teacher at school? He taught me that even the noblest concerto can be drained of its beauty and soul. And on the right is Bleeding Gums Murphy. He taught me that music is a fire in your belly that comes out of your mouth, so you better stick an instrument in front of it.
In El Tigre Manny had his dad, the hero White Pandera, and his grandfather, the villain Puma Loco.