I don't know much about Compete, but Alexa stinks. It's a small, self-selected group of users that in no way represents the Internet at large.

I'm not the only one who thinks so: http://franticindustries.com/blog/2006/12/18/why-alexa-sucks/

I've had questionable trends from either one. I can't say which I find more consistently reliable, but it'd probably be on a case-by-case basis on whichever results are skewed in my favor. ;)