Evangelion Movie 3: Q

Both movies have the crazy turn from the previous movies/TV series. In Rebellion and Evangelion 3.0, main protagonists found that their worlds has much changed than how it was in the end of their previous movies. Coincidentally, they are both the third movies of the saga and have the equally (in)famous talents behind them, Gen Urobuchi and Hideaki Anno. Both have this kind of enigmatic, "WTF is going on" feels and action scenes. 

Both popular stories feature an alternate change of time to feature a plot retaining the same casts revolving around the antagonists with similar elements putting the world at risk once more with different character personalities and plot developments that put's one shoes to the whole new level that allow nostalgia to flourish through our minds as we all grew up with watching the hit series to begin with  

Both have a boy that must try and handle the effects of a massive disaster, unknowing of what happen to the world and the people around it. Both boys get traumatized due to events in this changed world.  

Both bonds and sort of love between two boys are built, focusing the past and future of the world, try to save the world 

Space Runaway Ideon is one of the anime that inspired Hideaki Anno's Evangelion, since they both deal with similar themes. Both are dark and gritty science fiction anime, featuring destructive mecha that display their own will. They also have apocalyptic elements.  

I was reminded of Persona 3: Falling Down while watching this. Both movies have some sort of bonding between two boys trying to get to know eachother and become friends, both are also very depressing. Ryoji and Kaworu are also quite similar too, both eager to get closer to the protagonist (and some other spoiler related things, but that's for you to find out!). Needless to say, if you liked the relationship between Kaworu and Shinji in 3.0, you'll most likely be a fan of Ryoji and Makoto's relationship too. 

Both are alternate movie versions to TV series that are completely divorsed from the original plot, and instead focus on showing a darkest hour for the protagonist, who faces his greatest tragedy yet. 

Both are the third films in their respective film series. Both have a young mecha pilot as a main character, who is thrown in the front lines of war and has to cope with the experience of killing and watching people die, especially their loves ones. 

Both these series are each one of the very few who an inversion of the genre, or more specifically the cliches they're assumed to represent but turn them on their heads. They're an unrelenting, merciless, psychoanalysis that debunks the stereotypes, fantasies, and expectations set by the industry, and the audience themselves. It's a wake up call to the viewer, a revelation. The archetypes and fan service are pulled kicking and screaming out of escapism and thrown into a realistic environment, and left to die a magnificent death.  

Both are all about potent postwar commentary. Whilst eva only uses vague symbolism a couple of times to illustrate this. Terror in Resonance takes the root idea and runs with it. Both are in my mind very incomplete works but nonetheless are the most relevant modern examples I can think of to date.  

(As Nihon Animator Mihonichi is collection of unrelated stories, this recommendation is only for Me!Me!Me! part.) Both are trippy, mindfucking anime with excellent art and by same studio. Me!Me!Me! even has reference to Evangelion in it. 

Both are the third films in their respective film series. Both are mecha anime, featuring a young protagonist who has to pilot a mecha and experience war at a very young age.  

both are hard to understand due to some crazy plot twists and they both are mysterious.