I've been dominating in BGs with four enhancement shamans, even against the twinks. The enhancement have so much survivability that they have performed better than any other team I've ever played (I have not played DKs).

For PvE, unfortunately for some fights you need a magic dispel which means one shaman going resto for those specific boss fights. Otherwise, they haven't had any issues for me so far (early in MoP content to date). My pally team was better for PvE because pallies have even more passive healing, but either team can do just fine for PvE.

I dont know if DKs or shamans will be better for arena, but enhancement is the only spec we have seen so far that can global a toon. Personally, I think enhancement will be better for BGs, though DKs will be strong.