I. It is interestingly evident how this show is connected to Gurren Lagann; it's so very obviously a less polished precursor with inverted themes. Which isn't to say that Gurren Lagann does everything right that Eva did wrong--on the contrary, they both suffer from the same basic issue of engaging characters and moving story that is often subsumed to fanservice (in the loose sense of the word) and pandering. In Gurren Lagann, the fanservice was mostly in the form of fighting and yelling and generally appealing to the most annoying demographic of manhood-obsessed boys and young men. In Eva, the fanservice is mostly in the form of technobabble and philosophical maundering and generally appealing to the demographic of alienated emo teenagers.
Evangelion would have been better if they'd paid more attention to their budget (or if they had more budget; this is kind of a duh) and cut out some of the philosophical ramblings in favor of better developing the complex web of interpersonal relationships and utter dysfunction that characterizes the show's greatness. But not the crazy headtrips, or at least not most of them. Those were definitely necessary.
II. Like Gurren Lagann but moreso, Evangelion does both good and spectacularly awful things with gender.
First, the spectacularly awful. There's too much goddamn rape of the female characters--sure, you can argue that Shinji gets mindraped too, but it's not coded as a mental and physical violation the way it is with Rei and Asuka. Kaji's tendency toward sexual assault is played for laughs, and when he tells Misato that he just knows she really wants him even though she denies it, the text backs him up (which isn't to say Kaji is written to be without flaws--no major character in this show is--but his intended flaw is that, like Misato's father, he's willing to sacrifice himself for his work but can't bring himself to say "I love you" to and be there for a woman who loves him). Too many of the female characters come down in the end to their ties with men--most annoyingly when Ritsuko, whose main relationships up until the last few episodes have been with her mother and Misato, is revealed to be in love with Gendo. Misato is ultimately defined by her ties to her father and to Kaji (although she is my favorite and I think there's more to her than that). Female characters are defined sexually too often, which brings me back to the rape thing I started with.
Woman is very much a marked state in this show. On the other hand...man isn't entirely unmarked, either. The show obsesses over the idea of gender as a vast dividing line, which is itself rather poor symbolism considering that gender is really a messy and at times irrelevant spectrum.
But the fact remains that there are three lasting, significant male characters--Shinji, Gendo, and Kaji--and four lasting, significant female characters--Asuka, Rei, Misato, and Ritsuko. With the arguable exception of Rei, who I'll get to later, the female characters have distinct personalities separate from simply being love interests. You can say they have no agency, but it's debatable whether anyone has any agency in this show (although I won't deny that the way the female characters are deprived of their agency tends to be more sexual and more invasive/humiliating than the way the male characters are--see my entire rant above). This ratio is exceptional.
And then there's Rei.
People tend to argue, from what I've seen, that Rei is the biggest proof of Evangelion's misogyny, and on the one hand, yeah, there is some unfortunate subtext to be had in how disposable she is and how little agency she seems to have at first. But the interesting thing here is that to me, it doesn't seem like Rei was written to code as woman first and foremost, the way the vast majority of female characters (and certainly all the rest of Eva's female characters) are. It reads to me like she was written primarily as the embodiment of raw humanity, and her character arc is foremost about how she becomes a person. Using a female character to symbolize something so gender-neutral is refreshing.
Of course, that doesn't make up for how fucked up and wrong the way Gainax sexualizes her in merchandise is, but in the original show itself I don't think she's as sexist a character as she's often perceived to be.
So, in short, everyone at Gainax needs to interact with some actual women for once instead of obsessively sexualizing, debasing, and othering them in fiction...as usual. But if you can get past that, there are some interesting twists to the way Evangelion handles its female characters as well.
III. The themes are at times incoherent and disjointed, but that's to be expected considering the creator was headed directly for a nervous breakdown. At other times, they come through crystal clear. I think the most effective symbolism lies in the Angels, as messengers, as the Other that causes destruction simply by attempting to communicate with the solipsistic human mind.
Mostly, though, the rest of the much-vaunted symbolism would have been better invested in fleshing out the characters and their relationships to communicate the themes instead.
IV. My favorite character is probably Misato. I don't really dislike anyone except occasionally Kaji when they pull the sexual-assault-as-comedy-and/or-wisdom crap with him. I know Shinji is one of the most hated characters ever, but he mostly comes across as an everyman here, a vessel for the most general of human insecurities. It's interesting to note that everyone except Rei has what are essentially normal issues--fear of rejection, insecurity, hunger for attention, conflicted interests, self-loathing, flight from responsibility, parent issues--magnified to near-absurdity by the introduction of the Evangelions into their world. Rei (and for that matter Kaworu, but he's a minor character in the anime itself despite fandom's love for him) has the issue of learning to be human, of learning to have any of those issues in the first place.
Basically, every significant character in the series is simultaneously ridiculously dysfunctional and utterly normal, and that's an interesting twist.