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giant monsters invading town and it's up to a team of kids to save it

They start off with mostly normal action but get deeper later on. Their endings are often a source of criticism for both

weird shit just happens out of nowhere. both have visuals that can be pretty hard on the eyes, at least for me

In these movies the quiet main female from each story gives the main character a choice that determines the type of world they consider for themselves and as a result the main character goes through a phase of psychological conflict to accept their own decision. They're almost exactly the same in that way

Neon Genesis and Sangatsu no Lion aren't necessarily similar in terms of plot, but they do share similar psychological themes through each of the characters throughout their respective stories. And to state the obvious a depressed teenage boy as the protagonist has to deal with a feisty redhead and have characters named Rei in both shows