generally the differnece is packaging and the after sales support. Such as warranty and RMA process and how easy it is generally to deal with them if something does go wrong.
I would expect that 99% of the time that is nothing you should be worried about.
In addition there might be differneces in coolers used so different noise and heat performance, but as far as I know there are no non-reference coolers availabe yet for 6870.
As others have said, the only real difference is the sticker on the card, and the companies warranty\customer service if you ever have an issue. The biggest thing I look for when choosing a card, is it's warranty