Well I've tried to keep this spoiler free, so things are discussed in broad terms. There is a slight spoiler at the bottom (although it relates more so to the end of the first movie than anything really to do with the second movie) so avoid that if you haven't watched the first movie yet.
For the record, I was very impressed with the first movie. After watching it a number of times and not really looking into any discussion on the remakes, I was under the impression that the movies were going to more or less follow the series; a few changes/additions along the way but ultimately, the same story line. I went looking for reviews of the second movie for interests sake and ended up "spoiling" the movie for myself. I'm not one to let a few spoilers ruin a movie/game/series for me but I sure as hell wasn't going to wait around for a dvdrip to become available like I initially intended. I ended up watching the second movie as a cam rip.
Issues of video/audio quality aside (as is expected of a cam version), the movie itself is amazing. Whereas the first movie was essentially a remake of the first 6 eps of the series, the second film while covering the rest of the series, hardly resembles the original. While some key events remain the same (or at least similar), there have been huge changes made to the story line. As I said before, the movie covers basically every major event contained in the original series up until a fair way into the original movie (End of Evangelion). If you don't like cliffhanger endings, avoid this movie until the final two are released.
That brings me to my only real "complaint" about the remakes; while they offer answers to people who have seen the original series, looking at these two movies from the perspective of someone who has never watched NGE before, this definitely isn't the way to introduce yourself to the series. If the first movie was your intro to this series, hold back on watching the second movie until you've gone back and watched the original series (and movie). Hell, watch it a few times just so you can pick up on things you are bound to miss the first time around. While the second movie does give answers to a few things in the series, most of those answers bring up their own questions; the movie doesn't provide enough background information for new viewers to really pick up on some of the new concepts or even some of the original concepts.
As far as I'm concerned, these movies are no longer a retelling (compression?) of the original series but rather, compliment the original series. You really can't appreciate the series as a whole from just the movies alone (although this could change in the 3rd and 4th movies, I still think seeing the original series first is a must).
Anyway, the fight scenes are at the very least on an equal level to those in the first film (and are really, even more "over the top" in comparison). The character interactions/development is a lot better compared to the first (and in some respects a bit better than the series). The movie does suffer from feeling rushed in some scenes, since the series had the luxury of allowing scenes to "linger" for emotional effect/impact. Can't help but feel that there should have been a little more character development/interaction (once again, a lot of these scenes work well with having seen the series beforehand. A lot of the scenes seem to build upon "assumed knowledge" which I think makes it harder for newcomers to the series to appreciate some of these scenes).
One complaint I do have with the film is the horrible soundtrack. Some of the songs used just seem so out of place that it borders on ruining the scene. At the very least, some of the song choices can be very distracting. Hopefully they'll do another revision (similar to the eva 1.11 release) that adds a more appropriate sound track.
New character has a fairly minor role.
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Regarding the final scene of the first movie, something about it doesn't sit right with me. I didn't pick up on it until I read some discussion about it; Kaworu's appearance on the blood stained moon (think ending of End of Evangelion), the group of opened and closed containers. the appearance of another Lilith and Kaworu talking of meeting Shinji "again" raise some interesting questions. The second movie adds to this confusion with similar scenes of the moon base; something which wasn't included at all in the original series. The implications these scenes raise are interesting to say the least; the final scene alone makes the first movie worth the watch (for fans of the series anyway). The third and forth movies can't come soon enough.