AMD Radeon HD 7870 or nVidia GeForce GTX 560 Ti?
depends. for gaming- 7870 hands down.... if your using adobe software like premiere, etc, get the 660.....
560 is pretty old dude
Geforce if you need CUDA, PHYSX or Adaptive V-Sync. Radeon if you want GPGPU performance and better overclocking scaling. Can't go wrong either way, they're both good choices.
The 560 Ti is so old....
7870 is you're gaming, BitCoin mining, OpenGL and everyday use
660 for productivity, Adobe programs, PhysX, and other CUDA accelerated programs.