why would you switch to a six core with hopes it will improve game expirience most games dont use more then 3 cores anyways, dumb move. Either way you need to oc the heck out of the am3 chips to get great performance with a gtx 560ti (see my rig below). At least you got rid of the 465 which is a garbage/fodder card imo. As far as the cpu goes, what clock frequencies are you using?
Enable V-Sync (in game) and triple buffering (nvidia control panel) and that should eliminate all the screen tearing and most of the input lag.
beyond that I would stop playing WoW
sorry im just not an mmo guy