They compete over things that seem absolutely critical in your early twenties, somewhat impressive in your late twenties, and foolish at best by your mid thirties.
Eh, I joined one when I was 25 so I have to disagree. One of my fraternity friends followed me across the country and let me live on his couch for about two years. Another was my best man. Best friends I've ever had, easily.
Yeah the competition doesn't mean as much when you get older but you still get fired up years later on homecoming when you hear your old rival got more members or a bigger house or whatever.
I'm in my early thirties now and I still think it was worth it, competition and everything.
Who throws the best parties is just a small piece, an effect rather than the cause. Its who hangs out with the best sororities, who has the most power on campus, who's the biggest, who wins the most sports (which really is a meathead metric IMO)
But its not all pompous crap, they also compete for the best grades and the most successful alumni.
Fraternities are very elitist which is both good and bad, they try to find the best members, the most powerful attractive and smart guys on campus. If you have nothing to offer you probably won't be allowed in. What's offerable is anything that would help the fraternity reputation or finances.