I'm amazed that no one has actually made this recommendation yet.
Top wo Nerae is the Onee-chan of NGE by a good seven years. Both are works by Hideaki Anno, but NGE gets all the glory for being more recent (which is a shame in my opinion).
Top wo Nerae is a truly groundbreaking, character driven, Sci-Fi anime that is better NGE in many respects. If Top wo Nerae did not exist, then NGE may never have been made...
Both are powerful well written mech stories and Both are animated by Gainex,unlike it's later Sequel Diebuster,The first Gunbuster was more seriouse and payed more homage to Evangelion,both the first Gunbuster series and Evangelion both feature a lead who both grow from cowards to strong leads, Noriko Takaya from Gunbuster is very similar to Shinji Hikari from Evangelion,they may be crybabies at times,but they're likable and tolerable,Gunbuster is a cult classic worth checking out if you like Evangelion (Aliens,Angels, and Fanservice.....Oh my) and a bit of horror
Classic Gainax mecha anime that had a huge influence on the genre of mecha anime as we know it today.
Both are mecha-themed series created by Hideaki Anno. Though Gunbuster is seven years older, it already covers the concepts that formed the basis for NGE. Gunbuster does not delve in psychology as much as NGE, yet it tells the same coming-of-age story in which kids have to fight in real battles.
Giant super robots, massive battles against horrific enemies and unpleasable father figures! (And nudity!)
Hideki Anno created both Top wo Nerae! (Gunbuster) and Evangelion. Gunbuster is an essential for any mecha fan and a must watch for Evangelion fans because you can clearly see the prototypes for characters and ideas in Evangelion.
Coach = Gendo, Jung-Frued = Asuka, etc.
If you haven't seen Gunbuster, you can't understand what Anno is deconstrucing in Neon Genesis Evangelion.
You can easily see how NGE and TTGL grew from Top wo Nerae. It's as if a branching pathway was created by exploring the two extremes of psychological fear from piloting a giant robot and the over the top nature of the anime.
Gunbuster was also directed by Hideaki Anno, being his first work as a full director. As you watch Gunbuster, it becomes clear that some NGE concepts and ideas were born on Gunbuster, only to be fully developed later on NGE.
Gunbuster is far from being a work on the level of NGE (specially since it's only a 6 episode OVA), but if you liked NGE - specially how it was directed - then you should consider watching Gunbuster as well.
The first direction of Anno, Top wo nerae shares a lot of aspects with NGE (themes, characters, direction...), while in a denser package. A must-see for any SF anime fan (and a "watch-it-right-nao" for Anno fans).
Both star an unlikely hero who ends up saving people with a giant robot which the show is named after.
Both also ran out of money.
There are a lot of similarities between these shows. Main characters are similar and they have similar character arcs. Both deal with large robots fighting invaders from space, although NGE is mostly about combat on Earth while Gunbuster focuses on space battles.
As Hideaki Anno's first major seminal work, Gunbuster contains many of the themes and ideas that would later shape Evangelion, from character relationships to the hero's journey the main character goes through. Mecha action galore and some food for thought in terms of philosophical musings - you will find both in these anime.
Classic Gainax shows that made a major influence on the mecha genre and Gainax itself, with Gunbuster being more accessible and NGE being more psychological.
Both made by Hideaki Anno, mechs vs aliens, huge amount of attention to detail and science, setting up a tight and believable story with human characters and realistic moral conundrums.
Eva is darker/deeper, though Gunbuster has spectacular tits. Take that as you will.
Both are mecha series from Hideaki Anno with emphasis on characterization, drama and storytelling rather than action. It isn't as heady or as allegorical, which might be better for those who think Eva is too pretentious.
Epic and realistic sense of humanity effort to survive against crazy aliens.
Good Fanservice and cool fight.
Obviously, the works of an artist will share similarities and themes between them more often than not, and it is so with Hideaki Anno, too. But this goes further than that - it is inspiring in a way to have two shows that share so many and so deep similarities to yet be so strikingly unique in their own right. Don't delay watching the other one if you have seen one of the pair, as these shows are unquestionably linked and offer very different visions of two remarkable world that could have been the same if the retelling was lazy enough.
Both were directed by mastermind Hideaki Anno. Evangelion is closely related to Gunbuster, and you can find similarities everywhere. The camera angles, flashes, lightning... Both Shinji and Noriko are similar: they have a self-confidence problem and they resolve it by their way.
If you are an Evangelion fan or you enjoyed Evangelion, I heavily recommend you to watch Top Wo Nerae! Gunbuster, because is as great as the other.
Gunbuster was the directorial debut of Hideaki Anno, who would later go on to make this show. Although it lacks the emotional depth of Evangelion, it has amazing fights and a fun cast of characters. Not to mention it's only a 6 episode OVA, I think any fan of Eva should give it a try.