I definitely don't like NGE because it tries so damn hard to be deep and yet fails to be so, instead just throwing symbolism all over the place and trying to let the viewer piece together something out of the mess.
It also subordinates the setting, atmosphere, and to a lesser extent the characters to the plot, something I really dislike in any work of fiction, though this is entirely subjective. Basically every work of fiction that I greatly love either focuses on developing a well realized and gripping atmosphere/setting (Deus Ex, Looper, STALKER) or interesting and dynamic characters (Katanagatari, a few others that escape my mind at the moment), and then the plot follows from the development of the setting or the characters. NGE, meanwhile, has a setting that is largely undeveloped and a plot that is more or less an extended character study, except the characters are flat and uninteresting as all hell, and the plot doesn't smoothly follow from character motivations or the setting. I think a lot of the love it gets is for being a grimdark Anime back in the days when the tendency was to make relatively straightforward and more upbeat shows (with exceptions like Victory Gundam) if they weren't cheap, brainless gorefests.
Hell, while we're on the subject, I'll briefly go over a few shows that I've seen that I've wanted to bitch about for a while, but haven't had an excuse:
It had interesting ideas, and it does something fairly original and clever in the first episode. Unfortunately, it's mired by two issues that I had a hard time getting over:
-The visuals are a damn mess. All of the mech fights are CG, and they are horrifically bad CG at that. So about 1/4-1/3 of the show is really terrible CG mech fights, mostly against boring ass drones. Besides that, the character design is unsettling to me for some reason. I don't know if the eyes were improperly spaced or what, but a few characters looked incredibly strange to me at times. One in particular actually made me want to turn away whenever she showed up, and she was one of the more important characters so that was a hassle.
-Most of the enemies fought are super generic enemy drones, and a mech anime about fighting drones/robots is really damn boring. Closer to the end there is a particular scene where a character runs around the enemy battleship brutally killing everyone, and that scene almost made the grind of getting up to that point worthwhile, but it honestly wasn't enough.
A lot of good things that kept me watching the show to the end, but a lot of annoying things that bothered me all the way there. So I'll go over both of them:
+++The main character didn't just magically become super-duper stronk for no reason, he very, very slowly increased his capabilities over the course of the show. It's rewarding to see him grow until he's actually capable of holding his own to some degree.
--As a consequence of this, there is a whole load of filler. Like, a LOT of filler. I know you need some of this to keep developing characters and establish what new abilities the main character is getting, but I feel like they really could have cut down on the "protagonist lifting weights" and "characters go shopping and sit around idly chatting to develop character" scenes.
++Shana actually develops as a character to become more likeable as the story progresses instead of remaining "bitchy violent tsundere" for the duration of the show, something most of the shows that more or less copied her character apparently didn't notice.
--There's an obligatory love triangle thing in the show with some other girl, and an inordinate amount of time is wasted on this "WHICH GIRL WILL HE CHOOSE?!" subplot, but the show is actually named "Shakugan no Shana" so who the fuck do you think wins
+++There is a big twist that completely changes the dynamics of the show, putting characters on opposite sides while significantly broadening the scope of the show and clearing away most of the stupid filler shit
---Aforementioned twist was handled really fucking badly to start. Like, the third season starts, and the show basically goes "AND NOW THIS CHARACTER IS HELPING THE BAD GUYS" with no real explanation as to how it happened. Also, the main "villain" of the series isn't even mentioned to my understanding until this point, nor is his master plan.
-Previously more or less human Crimson Denizens, when made gathered into a large group, suddenly become super generic "humanoids with goofy animal heads". The only new characters introduced for their side that I even remember were Giant Electric Eel General and Double Gas Mask General.
-Artstyle is a bit weird. Characters have these ludicrously huge almost rectangular eyes that make them resemble praying mantises, but at least I was able to get used to it after a while.
-/+It has one of those "it would have ended reasonably well had we just stayed at home and done nothing" endings.