Well.... now that I think about it, maybe True North can just continue the tradition set by Calgary and keep the name of the team they originally yanked from Atlanta? The Winnipeg Thrashers actually has a nice ring to it, is already the name of a midget hockey team in that area, and (while I'm not sure of the migratory habits of of birds) maybe seeing a thrasher in Winnipeg isn't unheard of.
Barring that (admittedly unlikely scenario), the Jets seems like the overwhelmingly obvious choice, given how insanely popular the brand is in Winnipeg. I guess I could get used to the Moose, but Falcons just sounds so generic to me. Someone previously mentioned the Winnipeg Warriors, and that has a nice ring to it, but I doubt that they're really that interested in reaching back to their "ancient" history for a name.
So, all told, I guess I'd prefer the Jets, but it seems like True North is already set on keeping the Moose for some reason.