This review applies to the first film only..
I am not an anime fan. However, the constant raving about Evangelion made me bite the bullet and take a chance. So I bought a copy of the rebuild 1.0.
I loved it. It was dark and angsty, but not excessive. The misery was realistic and understandable (being that the whole premise of the show is to deconstruct the whole Falling-Into-The-Cockpit cliche and show how awful such a situation would actually be). The animation was impressive too.
I recently purchased the box set of the original series, and although the original and rebuild 1.0 are different continuities, I have to say I find the rebuild more effective. The tone of the first six episodes of Eva is lighter and more inconsistent, wheras the Rebuild is more forward with its dark approach. The fact that there is less space within a film (time-wise) actually means that the characterization is, in my judgement, more effective. It goes straight to the core issues of each character and doesn't pad things out. Yes, this may be dangerously close to
Flanderization, and some people may scream 'dumbing down,' but the overall effect is a starker characterization boiled down to the essentials.
What must be singled out for praise is the improvement in the production. The battle against Ramiel (the big diamond Angel) is absolutely stunning and very, very tense. Comparing against the original; there is no comparison.
In short, this non-anime-watcher would have to say the rebuild 1.0 is very much a distillation. The absolute essentials of Eva episodes 1 to 6 (with of course some changes for continuity purposes) boiled down to their tense, angsty, dark essentials. Consistent characterization, excellent technical detail, and a more mature feel make it quite clear that this work is fundamentally Evangelion.
Would a hardcore Eva fan like it? I am not in a position to answer that question. But I was impressed. Greatly.