Well, it depends on the competition. At CA MUni Weekend 2006, there was a "natural trials" competition, where a bunch of lines were taped out on the rocks, and the competition was won by whoever cleaned the most lines. (Shock: Kris Holm).
It sounds like this year's Moab MUniFest will have something a little more like "HORSE" (in a basketball context); someone sets out a challenge and others have to match it.
There have been timed uphill and downhill MUni races--usually done with one rider going at a time, although at NAUCC 2003 there was a mass-start downhill race on a grass slope. There was also a unicycle bowling contest on the same hill.