Rah'Xephon takes place in a world where aliens (or beings from another dimension, your call) called the Mu have taken over Tokyo, which has been imprisoned in a bubble called 'Tokyo Jupiter' that makes time move at approximately 1/5th speed. Ayato is a high schooler there who has a crush on a mysterious girl that no one else seems to realize is in their class.
One fateful morning, Ayato's world is called into question when mysterious 'Invaders' (actually regular humans), attack the city, and he discovers everyone he knows has blue blood. Furthermore, he realizes he is an 'instrumentalist', a Mu term for a pilot of a Xephon or Dolem (yeah, you guessed it, big golems made of clay that fill the Angels' bad guy shoes). Along with his kidnapper/rescuer/love interest Haruka, Ayato crashes the Rah'Xephon through the 'Jupiter' barrier, and helps defend the 'real' world against the Mu.
- The Xephon. Ok, it's definitely a new take on the mecha genre. It's made of clay and powered by the magic of singing. Not my bag, but it's new, and it has a sort of internal consistency that a lot of pseudo-science mecha stories lack.
- Combined arms. After watching Evangelion where practically nothing but an Eva can even scratch an Angel, watching the Alpha squadron fighter pilots, and even big sci-fi tanks have some effect against Dolems and the Mu fighters is kind of refreshing. The employment of unmanned drone fighters, static anti-air defenses, fighters, tanks, and later Alpha squadron Mecha as multiple layers of intercept gives the defense against the Mu a very real world feel.
- Lower emotional investment. There are times when it actually gets annoying how calm the characters are (the soft monotones during dialogues can get tedious), but for the most part, watching Rah'Xephon after Evangelion gives you the impression that Prozac must be in Nirai Kanai's drinking water supply. Seriously, this show is like Eva with mood levelers. These folks can take stuff in stride that would cause an Eva character to have a crippling emotional breakdown.
- Time Lapse. Flashbacks, time bubbles, or alternate dimension plot threads are annoying to many viewers. While this taints a lot of anime for many, as these are used pretty heavily in this genre, Rah'Xephon does do this quite a lot, to the point where there is some difficulty remembering who really knows what. Was person 1 really there or was it part of person 2's hallucination?
- Sibling Rivalry. Everybody in this freaking series is related to everybody else. And not. It becomes difficult to keep straight who is related and who is not actually related, because certain characters call everyone brother or sister. Including their brothers and sisters. Throw in the tendency of the Japanese to call older people they know aunt or uncle, and this becomes a very serious morass of familial ties. Including a few love interests. Eww.
- Everybody loves Ayato. Almost as annoying as the 'Everyone loves Shinji' dilemma. Really, all the women in this show are into this kid. At one point, two mature, adult fighter pilots (who are both aparently quite older than Ayato) get in a physical altercation over which of them are going to pose for him to paint. Seriously. Even more confusing is that the most attractive woman in the series, the mysterious assistant to the even more mysterious professor, is the only women NOT into Ayato, and is completely spurned by every male in the show.
It's a pretty fun series. There is also a movie adaptation, which is sort of like Eva 1.11, a synopsis flick.