Mmm, I think it's both envy ("Reed is smarter than I am.") guilt ("Deep inside, I know Reed is a better person than I am.") and jealousy ("Everyone loves Reed but no one loves Doom!") all combined with an ego and a pride the size of a planet that keeps him from ever acknowledging any of these facts.
I think coupled with that is that Reed and Doom are both on a totally different level from the rest of humanity, in a sense they are the only humans who can talk to each other without dumbing things down for the benefit of the audience. Whenever Doom and Reed work together you get the feel that there's absolutely NOTHING they couldn't do together. And Doom HATES that, because it means that he isn't perfect alone.