Apparently Dershowitz is a pro-Israeli (and US National Security) Jew, while Finkelstein is an anti-Israeli self-hating Jew who is allied with Noam Chomsky and Alexander Cocvburn. The areas of dispute include ancient and modern history and foreign policy, anti-semitism and civil liberties, and scholarly values. As might be expected from the above, the arguments are complex and varied.
Without going into this briar patch I say, go with Dershowitz.