Accidental Innuendo: GX's tagline is "Believe in justice and hold a determination to fist." In common American slang, "fist" as a verb means... something very, very different from what the creators probably intended.
Hibiki was rather divisive during the first season. While some viewers found her to be spirited and heroic, others generally considered her to be contrived and obnoxious. G improved her standing with consistent morals and general kickassery.
She falls back into this in GX, when her unwillingness to fight is brought to the forefront. Arguments abound as to whether her angst is justified or just Wangst, and whether her reasons for hesitating make sense given her prior development or fly in the face of that development. In particular, her snapping at Maria and subsequent apology after the latter saves her from Garie are seen as either justified frustration bubbling to the surface at an unfortunate time, or just her being ungrateful and selfish. She still manages to be incredibly more badass as ever.
Pre-character development Tsubasa was often considered to be bitchy. Post-character development, she's far more well-liked.
Many fans are divided as to whether G's penchant for over-the-top cliffhangers and plot twists improved the series and made it more fun, or whether it caused the story to collapse under its own weight.
As of GX the fanbase is divided as to whether the heavily episodic nature of Episodes 7-10 are giving characters (especially the FIS girls) development that they sorely missed in G or if they're making the show too predictable and stifling everyone's development by cramming them into glorified Monster of the Week plots.
Both Ver and Fine are redeemed by the season after they appear though: Fine pulls a sacrifice to save Shirabe from Igalima's Soul Reaper, whereas Ver plays a huge role in disabling the Chateau, reconstructing the world, and possibly finding a way to allow the FIS trio to fight with the 2nd Div trio without LiNKER - this last is EXTREMELY crucial as it means that they can now activate their Climax Song without instantly going down for the count. However, Ver still veers in monsterdom as unlike Fine, his newest actions are still driven with selfish motives of making himself the hero of the world, proving that maybe you're not scots free from the trope even if you pull a Heel–Face Turn...
Contested Sequel: GX is beloved by many fans - but just as many are baffled at its popularity. Common criticisms include unlikeable antagonists that the show nevertheless tries to portray in a sympathetic light, bad fights with focus given to power level wank and one sided curbstomps over decent choreography, most of the cast being useless and barely doing anything outside of their focus episodes, and pacing issues.
Micha, the last of the Auto-Scorers to appear, was receiving attention online before her official debut in the show. Her shark teeth and manic behavior in the OP may (or may not) have had something to do with that.
On the subject of the Auto-Scorers, Garie has built a dedicated following due to her smug, sarcastic personality and amusing facial expressions. It probably helps that in the first four episodes of GX, she has been the most prominent of the Auto-Scorers following her introduction.
Dr Ver from G is a fan favorite villain amongst fans, due to his over the top and hammy nature as a villain, with some downright insane crazy expression, which seem to somehow benefit from being Off Model, emphasizing his batshit insanity even better. This may be the main reason why he comes back in Episode 9 of GX. It also certainly doesn't hurt that he's voiced byTomokazu Sugita.
The majority of the fans who watched the first season found the sequel to be superior after a few episodes had aired, due to the increased action, an antagonist group that has been around since the beginning and most of them are developed Anti-Villain... and compounding them is Dr. Ver as the Big Bad.
In fact, it's seen as so much better the Blu-ray sales for the first volume were more than double of that of the blu-ray sales of the first season.
GX has proven to be more popular than the first two seasons and there have been even more preorders than other series who launched at the same season. Reasons for this are the amazing songs, much more action and surprisingly interesting and dangerous villains.
Maria and Tsubasa in Season 2. Not only is Maria's Symphogear identical to Kanade's, their duet in the first episode is awfully suggestive, with furtive glances and both performers stroking their long, phallic microphones. Once Maria is revealed as a villain, she and Tsubasa directly oppose one another, with their fights being some of the most intense.
The opening of G has two silhouettes at the beginning, with one of them trying to catch the hand of the other. The silhouettes are Hibiki and Finé.
Garie is a Ensemble Darkhorse. Before she was introduced, fans speculated her being the most boring Auto-Scorer due to her lackluster design. Then they learnt that she isn't just a big-eyed doll with a big smile.
Love to Hate: Both Big Bads, Finé and Dr. Ver are well received by the fans. Even though they don't fit the Magnificent Bastard category, their hammy portrayal and their manipulative abilities have cause the fanbase to like them or to hate them. Especially Dr. Ver is considered as an over-the-top villain, being much crazier than Finé herself, even though Dr. Ver is a weakling compared to her.
Moe: Hibiki and Miku both definitely qualify as this.
And, come season 2, Kirika and Shirabe both climb onto the Moe bandwagon.
Not to mention, Chris became a lot more Moe during Season 2.
Carol in GX, with her short stature and Cute Witch attire is definitely this, to the point where some find it hard to take her seriously as a villain.
Not to mention Elfnein, being an even cuter and innocent version of Carol.
Moral Event Horizon: So how do you think Ver can top Fine in terms of being utterly despicable? Well, a good starter sign of skirting the line would be when he fetches Noises on passing by kids just because they were looking at him fetching Noises to US soldiers with a smile on his face. If that wasn't enough, then forcefully injecting Psycho Serum to Kirika and Shirabe and tells them to use the Swan Song (which would mean death for them) while acting like an Entitled Bastard despite their pains and dangers of getting injected with them would be him crossing the line. Kidnapping and brainwashing Miku into giving her a Symphogear form? Now that's leaping faaaar away and deeper from the horizon, accompanied with the biggest "WOO-HOO!" you can ever imagine. He's still waving and taking another leap when he sends Nastassja off to the moon, killing her, because she's trying to avert the damage he's caused, this is also the final push for Maria to finally have enough with bearing with him and deciding to kill him.
Carol may well be trying to top Ver in season 3. Rather than explain herself or her position to Hibiki, when the latter finds her at the site of a major fire and voices her intention to come to her aid, she blasts the latter with energy cyclones, to try to force her to fight, purely for the purpose of stripping away her Symphogear, which is well known to be her sole means of life support. When attacking Hibiki directly doesn't work, she sends her Autoscorers to attack anyone near Hibiki to try to provoke her. After forcing Hibiki to fight by directly threatening Miku, an unarmed civilian, she then only defeats Hibiki because Hibiki was fighting Autoscorers two on one, but that still is not enough. While Hibiki is comatose, Carol sends all the Autoscorers out to destroy the power supply to the hospitals where Hibiki might be. And lastly when Shirabe and Kirika come out to protect the Medical bay where Hibiki is staying, Carol doesn't just order her Autoscorers to disable the girls' Symphogear, but explicitly tells them to "do whatever [they] want" because the girls are "uninteresting." Oh, and that Freudian Excuse? Turns out those people are long dead, as in dead for centuries, and Carol's desire to "kill a miracle" by dissecting the planet has nothing to do with her father's dying wish, as she originally claimed. If that doesn't convince you, then Episode 12 would instead: After Elfnein translates that her father's true wish is to forgive the world and that is the true key of understanding the world like what alchemy was meant to be... Carol instead just flat out refuse to honor that, choosing to still hate the world for killing her father and goes on ahead anyway with her attempts to destroy the world for nothing but self-indulged vengeance.
One True Pairing: Hibiki and Miku since the first season and Shirabe and Kirika since G. Tsubasa and Maria almost crosses this thanks to their moments together in GX.
Hibiki nearly became The Scrappy because of her poor performance during the first four episodes. Episode 5 rescued her, and the second season increased her popularity.
Maria finally getting over her indecisiveness and getting stuff done in the finale improved her status among viewers. GX improved her standing as she became more decisive and her battling of the Auto-Scorers despite the disadvantage, especially after she manages to beat Garie solo with a new Gear, in IGNITE mode, after failing to activate it at least once.
Kirika has become a lot more popular after her Big Damn Heroes moment in the third episode of GX, rescuing Chris despite the risk to her body caused by transforming without LiNKER.
While he's most likely the most hated character of the season, to some, Hibiki's father is considered slightly redeemed during the encounter with Carol, whereas all his cowardly acts turns out were meant to be a Heroic Sacrifice so Hibiki can live and fix the family while he's gone, and he actually decided to man up, face his faults, actually helps Hibiki transform and then watch her battles from afar with complete faith.
The Scrappy: It's rather ironic that those who owned this status somehow get redeemed as seen above. But, to list their original faults...
Ryoko got a lot of hate during the first season, largely for being a Psycho Lesbian.
And for season two, Maria has become one of these. She started the season with a lot of love in part due to fantastic songs and being voiced by Yoko Hikasa. Badass Decay and failing to get anything done plot-wise gained her a great deal of hate.
Quite a few people were annoyed by Kirika's actions in G, thanks to the subplot about her becoming Finé, which was ripe with Wangst and bad decisions. And it turned out that Shirabe was Finé all along, which made the clumsy writing completely pointless.
Hibiki's father, who abandoned his family after the concert disaster in Season 1, makes his first in-person appearance in the show in GX. In his first shared scene with Hibiki, he not only refuses to apologise, but asks for her help in trying to get him back with Hibiki's mother, and at the end of the conversation leaves Hibiki with the lunch bill. His later appearances do nothing to endear him to fans either; while by the end of the series Hibiki has forgiven him and he actually did some genuinely good and protective actions on Hibiki to regain that trust (and even she reintroduced her to her mother, who doesn't seem too happy at the prospect), he's still probably the most reviled character in the series among fans.
The Woobie: Hibiki seems hit VERY hard by the Woobie stick in GX. While her backstory was already hinted at in G, it's only in GX that we see just how hard her backstory and experiences contribute to her being a Stepford Smiler that's too close to the edge. She loses it twice big-time in GX - once when Maria is forced to fight on her behalf and another when she runs into her estranged father.
This crosses into Tear Jerker territory when the other Symphogear users want to help and comfort her but can't because they don't know what it's like to have stable family relationships. Tsubasa's dad consistently treated her as a tool of the Kazanari family (and her mom is completely absent from the story), Chris never knew her parents because they died when she was young, and the F.I.S. Children don't have any relatives to speak of, with Maria losing her younger sister years prior to the events of G.