Both shows deal with teenagers and their psychology, both have supernatural elements that are used symbolically, both have further and constant symbolism throughout each episode, both address philosophical issues while still having some comedy elements,(and both have a penguin sidekick.)
Both are mutilayerd mindblowers.
While these shows are very different (Mawaru Penguindrum is more 'fluffy'), they both make effective use of symbolism (with some of it, in both cases, revolving around religion) and explore meanings of both love and sacrifice. However, the characters in NGE are more believable and their insecurities are explored i a much more detailed level.
Some people might see this recommendation and go "wtf is wrong with your head? the two are nothing alike!" and yet, when I was looking for an anime that was similar to mawaru penguindrum, neon genesis evangelion came to mind instantly. True, in MP, there are no fight scenes, nor are there post acalyptic monsters out to destroy the world. (there are mechas though--erm, kinda)
What they do have in common, however, is the complexity in the story. This one's a recommendation for people that like scratching their heads a little when they watch a good show. You cannot simply watch either without thinking; everything
Both have a very very huge amount of symbolism in them. To different extents. As with other Ikuhara shows, Penguindrum definitely lives up to it.
To those who appreciated the intense symbolism and quirky, intresting characters with more depth then meets the eye, look no further.
While Pengiundrum's story is alot different than Evangelion, there's no denying the similarities to be found here. Honestly, as I watched Penguindrum I couldn't help but feel like it is a sillier, if not MORE intense, version of Eva. Minus the mechs....
Both have some pretty trippy and wild moments in it and focus on a girl also getting caught up in some strange events too throughout the story but things do get serious from time to time as well too.
both of them have unique atmosphere and artstyle. Penguindrum is a must watch if you enjoy simbolism and teenagers having mental breakdowns, also, penguindrum has an amazing OST, i assure you will enjoy it, just give it a try
Though Penguindrum isn't action, much less so mecha, they're both surreal psychological dramas (with Penguindrum being a bit more dramedy than EVA). They both become darker and more complicated as the series progresses. The use of symbolism and surrealism especially tie the two together and a plot that probably won't make too much sense until the credits roll for the final time, or maybe only some time after that.
If it was the surrealism, symbolism, or occasional experimentalism and mindf*ckery that brought you to one, you'll most likely enjoy the other.