AMD Radeon HD6850 or Nvidia GeForce GTX 460

Gigabyte is a decent brand, is there a specific reason why you're stuck to them as a brand though? Such makers as MSI, Sapphire, XFX, EVGA and Palit make these cards and price competitively.

Anyway, according to the hierarchy chart, the 460 and 6850 are on equal footing with each other, so it would really come down to what you can get for the best price i guess. I personally would go for the 6850 as it's in the newest generation family of ATI cards while the 460 has now been succeeded by the 560 which will (i'm guessing) be out of your budget.

So for me it's the 6850, but from what you said you're going to do with it, I can't imagine either one will be a bad purchase as they both work very well. I would suggest you take a look around the online retailers you purchase from and see what other vendors are offering their cards at as you may get a better price for essentially the same thing.

There isn't a specific reason I've chosen Gigabyte. I've just been looking at a number of reviews on other brands and it seems like the GB would be a good option.

I've heard that XFX has been sliding with their version of the 6850 so I ruled that out.
MSI was said to be not as good as the GB so I, once again, ruled that out.
However, Sapphire and EVGA are still in the good books for me so I would change to either one of those if they're better than the GB ones. I haven't heard many things from Palit so I didn't really consider them.

But anyway, thanks for your opinion! I'll probably end up getting the 6850. I've been tipping towards it from the beginning but I just wasn't sure.  

Yeah unless you just want the benefits of some hardware Physx support, might as well nab a 6850. You wont regret it, as it is a very well rounded card performer.

That's fair enough, Sapphire or Gigabyte 6850 will be lovely.