To dust off an old idiom, it's like comparing apples to oranges. Google Wave and Yoomoot both try and to revolutionize the way people talk to each other. But that's an extremely broad category. Google Wave tries to draw on the tradition of email, instant messaging and chatrooms. It's trying to combine and outdo them of course, but it's the same basic idea. Yoomoot on the otherhand, is easily identified, both by the designers and the users, as a fusion of things like wikis, forums and comment pages.
These are fundamentally different mediums. Google Wave is one on one, or at most, a small group. Yoomoot on the other hand is more ambitious in that it tries to tie together people with no real personal history. To boil it down, Google Wave is about people, Yoomoot is about ideas.
Even if both were to take off and become absolutely dominate, I doubt there would be much in the way of crowding or toes being stepped on, because they simply occupy different continuums.
not wanting to sound jealous or anything...
Imagine everybody could see everyone else's 'waves'? The result would be an utterly overwhelming mess. Wave is principally designed as an email replacement, so it's focused on private collaboration between small groups of people.
yoomoot meanwhile works for both small groups and immense groups.
yoomoot may merge wikis, bookmarks, comments, blogs and forum posts, but it doesn't have instant messaging. Wave does.
Google Wave discussions are done via 'traditional' threaded comments. This leads to mess. Yoomoot ensures discussions are navigable, concise, reusable, focused and civil. Google Wave ensures makes discussions potentially more concise (because of the editing features) but this paltry compared to Yoomoot's discussion-organising obsession. See http://yoomoot.com/the-seven-sins-of-online-collaboration/ for more details.