Hard core all the way. I can't stand putting a full mag into someone and still not killing them. Besides that people in core have found out that snipers are one shot guns so in the clan ops that's what most of the teams are using.
I prefer core myself. I think hardcore is a place where people just sit and camp all match. I really enjoy league play on this Black Ops. The game types that stick out as my favorite right now are Hardpoint, Domination and Team Deathmatch.
I highly prefer hardcore, but have played more core purely due to the fact that that League play is only core. I've also been trying to play with some more of the clan members and thus I have played a bit more core. Overall I prefer HC:TDM.