Ye gods! Annihilate but space and time,
And make two lovers happy.

Thus Alexander Pope paraphrased a poem by one of his contemporaries in Peri Bathos, or the Art of Sinking in Poetry. It’s a good summary of RahXephon, too.
RahXephon starts off as nicely complicated science fiction. A few years before the story starts, Tokyo was cut off from the rest of the planet by a dome-shaped force field. Ayato is a high-school student there who paints a picture of a girl in a yellow dress. Many things happen quickly — Tokyo is attacked, gunmen try to kidnap Ayato, he is rescued by a strange woman with impressive fighting skills, he meets the girl in his picture, he finds a gigantic egg that cracks to reveal what looks like a 150-meter tall mecha, he discovers that his mother has cobalt-blue blood — and Ayato soon finds that eveything he knows is wrong. Time flows differently in Tokyo; in the rest of the world, it’s 12 years later. Humanity is under attack from the “Mu,” whose “dolems” appear out of nowhere. These dolems — one source says the name is derived from “golem,” another says, “do, re, mi;” either is plausible — are giant, singing statues floating in the air whose “arias” render vast areas nonexistant. They attack in other ways, too. RahXephon — the giant mecha-like entity that Ayato discovered — fights more effectively against the dolems than anything the Terran forces have, but only the unmilitary Ayato can pilot it.
It eventually becomes clear that RahXephon is fantasy, not SF, and magic, not physics, keeps the dolems aloft and powers the RahXephon. It also becomes clear that the central narrative is actually a love story. Before advent of the Mu, Ayato had a girlfriend. The dome that cut Tokyo off from the rest of the world was created while she was on a trip outside of Tokyo. She’s now twelve years older than Ayato, but she is still fond of him. However, somebody or something fiddled with Ayato’s memory, and he doesn’t remember her.
For a while RahXephon promises to be a superior series. The writers, headed by Chiaki J. Konaka, spend as much time developing the characters as they do on action and mystification. The art, character design, animation, voice acting and music are well-done, and the opening theme, “Hemisphere,” composed by Yoko Kanno and sung by Maaya Sakamoto, is a favorite of mine (view the “production sketches” on each DVD to hear the full-length version). There are problems with logic and consistency, and I wished occasionally that Ayato would grab a few lapels and demand, “Who? What? When? Where? Why?” but these flaws would have been forgiveable if the series had ended well. Ultimately, though, the solution is not worthy of the mystery. Although most of the questions are answered — sorta — conflicts resolved and scumbags shot, the answers are not really satisfying, and I consequently can’t give RahXephon more than a lukewarm recommendation.
I’ve never seen Neon Genesis Evangelion (and I’m in no hurry to do so), so I can’t compare it and RahXephon.