I personally prefer the original Evangelion TV series, warts and all, over the old Eva movies or even the new movie series. But I'll tell you one thing the new movies have that the original TV series doesn't: Pirate Asuka fighting an Angel in space. You can watch the first six-plus minutes of Gainax's newest installment of their Evangelion retelling above; the first minute is kind of a bust, but after that... ye gods, is this movie pretty. Hopefully it won't be too long before Funimation is allowed to license it for North American audiences.
Oh, a warning: The dialogue is all in Japanese and there are no subtitles. However, I imagine any Eva fan will be able to glean the meaning when Asuka screams "Baka Shinji!" near the end.