USAGE : mostly gaming(i play mw3, bf3, dota2, but also love 2 play all new games.. atleast i try them all once)
my pc is on 24X7. I play games or watch movies/TV series etc.. when m sleeping torrents are on.
ADDITIONAL COMMENTS: need gpu mostly for play new titles. i don't have any preference, amd or nvidia both will do, and gpu should have good cooling system because here room temp. goes to 40 C in summers. 6950/560ti are too expensive so don't want them.
this is mostly a personal question... nvidia or ati, i've already had ati video cards, and i know they lack in some stuff no Physx/Driver Problems/Games need specific patching/no 3D Vision, with my experiences from that time, i don't buy more ATI'S but like i said, this is personal, lots of people would choose go for the ATI instead.
The best thing for you to do is read the pros and cons and see what fits better in your profile (will you need physx?, will you play in 3D?, do you care in downloading a fix patch when the game don't work?)
I would certainly go for 560... but if i were you, i would take more money and go for 560ti, i have one and it is great.
Two recent releases (BF3 and Skyrim) had working nVidia drivers before working AMD drivers, but both companies have had driver issues from time to time. Check the benchmarks of the specific [types of] games you play, and see if any of them prefer one architecture over the other. I'm running a GTX560Ti myself, but honestly if it croaked I'd probably get a HD6870 or HD6850 because my games aren't extremely demanding (except perhaps Skyrim, but I think I could "suffer" on high rather than ultra settings).
I know you don't want to hear this, but for a game like BF3 which can be pretty demanding I wouldn't go lower than a 560ti or preferably a 6950 1 gb. You are gaming at a pretty high resolution which is going to be even more demanding.
On to the answer to your question
You can't go wrong with either card. They both play at near the same fps and have had driver revisions to optimize their performance.
Here is a quick look at how they size up at a lower resolution:
hd 6870 will be better for gaming and it can get upto 5 fps more in the game then the gtx 560 and the non overclocked gtx 560ti is not too much better then hd 6870 if ur thinking to buy an graphic card cheaper will be better so the hd 6870 will be more better option to get hd 6870 because of its performance and price.