To my mind Wave is about getting stuff done while Facebook is about
hanging out. Facebook is actually terrible for managing projects
whereas Wave would be great; well, a lot better than existing email and
Facebook at any rate.
Facebook is designed for nosiness, social
parading and general frivolous socialising. Wave could do some of that
but it just doesn't seem to designed for it. From what I understand,
waves are like emails in that you specifically decide who they are
shared with, but you also have the option to make waves completely public. This is very different to Facebook where everything is, by
default, shared with your entire network but nothing is completely private.
To me, the private-between-a-select-few or completely-public model is well suited for collaboration (you work together to build something and then publish it) and the second is suited for socialising (you want your friends to be generally aware of what you're doing, but only if they're interested - you don't want to specifically contact them about it; and also you don't want Joe Public, Sam the Boss and Grandma Doesn't-Appreciate-Drunken-Photos to know what you're up to. Again, Wave is suited for focused collaboration and Facebook for vague socialising.
The only area I see real overlap between Wave and Facebook is
organising events. So I think Wave may undermine Facebook's usefulness
as an event-organiser, but that's not exactly going to kill it.
I
think Wave would only be a competitor to Facebook if the third party
apps part of Wave really took off crazily. If that happens I can barely
imagine the possibilities. But I think it's unlikely and I doubt Google
is betting on it.
People have such large established networks on Facebook. Most people will have no reason to move to Wave to do the things they can already do on Facebook.