I don't think either team is really in line for a "rebuild." Not if you take that word seriously, anyway.
Chicago is making some changes. They traded a roster player for a 1st rounder recently (Hartman to Nashville). And that's about as intense as they are going to get to change the roster and build for the future. You won't see them move out Toews or Kane, ever. So they will try to compete, and rightly so, for the foreseeable future.
LA is much the same. Actually, they need a "rebuild" even less. They just added Kovalchuk to push to win now. And they have Kopitar and Doughty in their prime right now. No reset button on the horizon.
I guess I could still answer the question, and say Chicago. But we're talking about a rebuild that might not start until like 5 or 6 years from now.