I'm going with Cleveland in a squeaker.
LeBron comes through in the end and the Cavaliers steal the first game. I expect a very physical battle in the paint, with Duncan getting his points, but having to work harder on both ends.
The Spurs will have to choose whether to double LeBron or not, and if so, how. When Detroit doubled him. he dealt out assists and the other players stepped up. In either case, the Spurs have to prove that they can stop Cleveland from scoring.
The Spurs success depends to a great extent on Parker, and if the Cavs can keep him out of the paint. By controlling the boards, they can control when or if the Spurs can run. Also, Ginobli who is so unpredictable, that he can break down defenses. In their regular season games, the Cavs were able to keep the Spurs in check.
I really think the starters should offset each other, with the Spurs bench having the edge in depth and talent.
But I think it will be the Spurs that have to find a way to adjust to the Cavs, because they match up so well. Cleveland naturally will put a lot of pressure on the Spurs than they've been used to. The Cavs are physically bigger. That is what will give the Cavaliers the edge they need to win.
This doesn't mean the Cavs win the series, either, just that LeBron is going to be irrepressible in game 1.