What is the relationship between Neon Genesis Evangelion and RahXephon? I have watched both Neon Genesis Evangelion and RahXephon. Since they have the same story and the same structure, I think that RahXephon is a copy of Neon Genesis Evangelion. 

What is the actual relationship between Neon Genesis Evangelion and RahXephon?
The creator of RahXephon, Yutaka Izubuchi, admits to having heavily used Brave Raideen as the influence for RahXephon. There's a really great interview of both Izubuchi and Anno (creator of Evangelion) that's really revealing about the influences between the two. Relevant quote:


  Mr. Izubuchi said before that "Eva" was Combattler [Chōdenji Robo Combattler V] and RahXephon was Brave Raideen, didn't you? 


If you read the entire interview, it never insinuates that there was any copying of Evangelion in Rahxephon. Instead, these are two contemporaries who believe they are equals that have both been influenced by the same shows, like Mazinger, Combattler V, Tokusatsu, Gowapper 5, etc.

Eventhough they never directly admit it, I'm sure there's some amount of influence that Evangelion had on Rahxephon, intended or not, simply because Evangelion was an incredibly influential show, at a time when it seemed anime in general was stagnating. So everything that came after that, for better or worse, could have had some influence from Evangelion.

With Rahxephon in particular, your mileage may vary on how similar the shows really are. If you've seen Brave Raideen, you'll instantly realize that the show is pretty much a modern spin of that old show, while a lot of that spin could be argued to be influenced by Evangelion. There's some people who believe it's a blatant rip-off, but Izubuchi doesn't say that it is, and Anno doesn't seem to think the similarities are even worth mentioning.