First, I do agree with that video that Evangelion was better at leaving more of an impact since it was more subtly psychological while animes like Elfen Lied are trying to be, but instead are ridiculous shock value for the sake of shock value with the excessive nudity, dismemberment, and puppies being killed. So as a result they're too unrealistic to leave a mark and are inadvertently hilarious. (Plus the KAWAII art style clashes with the dark mood and makes things even worse.)
Sometimes, insanity needs to be approached with more care in order for it not to be comical...or at least too typical. A slow build up of unnerving behavior is much more disturbing than a manic person with a slasher grin randomly cutting up people for the LULZ.
I'm going to use the movie There Will Be Blood as an example. It's not really a horror, it's more of a disturbing drama about this guy's life, yet I found it MUCH more creepy than a lot of straight-up horror films. The entire movie reveals to us in bits in pieces how unstable the main character is just through his words, actions, and behavior towards others. He only has a few of moments where he actually does anything truly violent, yet he creeped me out far more than any blatantly obvious knife-wielding anime girl could.
So yes, when it comes to "messed up" in terms of insanity, these are my thoughts on the matter.