GTX 650 has 2gb GDDR5. It has a higher Effective memory clock, and a higher core clock.
Gtx 650 looks nicer and costs 169.99 on NewEgg
Effective Mem Clock: 5650: 5400MHZ 6850: 4000MHZ
Core Clock: 5650: 928 Mhz 6850 700MHz
GTX 650 uses a higher level of OpenGL scoring in at 4.3 and the 6850 has 4.1.
The GTX650 is succeeded by the 6850 in terms of Memory Interface. The Gtx650 has 128 bit whereas the 6850 has 256 bit.
They both are 6 pin, meaning they require to be plugged in by the PSU. 6850 needs a 500 watt or greater PSU. The 650 needs a 400 watt.
If your motherboard is a bit old, it wont support the GTX 560. Since it uses PCI-E 3.