My quick comparison:
Sales reps: CC, hands down. Most of the BB reps I deal with are moronic tools that are lucky they can get both legs into their pants without requiring a diagram. They're also not the most friendly of people. CC reps tend to be much more friendly, clued in to their store and sales and wanting to serve the customer.
Customer service: Tends to be a toss up, though a nod goes to CC's more reasonable PM policy that doesn't require two trips to the register to get 10% at day of purchase, plus they'll PM to 10% off their own pricing. CS reps from both places tend to be about as equal. PM's are much less painful with CC than BB, without question.
Sale pricing: CC blows BB out of the water, figuring we've had multiple cheap gaming deals in the last eigh months from CC and one from BB. GGC from BB is nice, when you can find the $19.99 variety, and currently, it's even more attractive, though that can change quickly.
Merchandising and store upkeep: CC edges out BB, since they tend to be a little more clueful about when the store looks like a complete pile of crap, though organization and merchandising skills tend to be a little lacking on both sides of the equation.
Corporate office assistance: More issues for me get handled lower down the hierarchical ladder with CC than BB. Higher up, they're about equal. BB does happily bend over backwards and offer your GC's when you have them in the wrong.
Knowledge of their own policies: CC seems better on this than BB, since I tend to know policies and procedures at BB better than the average BB rep/CS rep, with it happening less with CC.
Overall, my preference is for CC over BB, without question.