Is PCI 2.0 x 16 and PCI 3.0 x 16 compatible?
I would like to use the gigabyte GA-970A-D3 with the Zotac ZT-60802-10p GeForce 660ti are the two compatible?
Short Answer:
Yes, they are 100% compatible.
Long Answer:
PCI-e 2.0 and PCI-e 3.0 both use the same slot on a motherboard (a PCI-e slot), but are just different versions of the interface between the card and the motherboard itself. PCI-e 3.0 is the latest version and is twice as fast as PCI-e 2.0.
The "x16" means that it uses 16 lanes in the motherboard for speed, so x8 is half as fast as x16 because it uses half as many lanes. Since PCI-e 3.0 is twice as fast as PCI-e 2.0, PCI-e 3.0 x8 is the same as PCI-e 2.0 x16 in speed.
A PCI-e 3.0 card will work in a PCI-e 2.0 slot and vice versa, so they are completely compatible with one another.
Performance-wise, there isn't really a difference between the two right now. There aren't any Graphic Cards that can fully saturate (read: max out) PCI-e 2.0 x16, so whether you are using 2.0 or 3.0 does not matter as it won't affect the performance of your system. One day we might have Graphic cards that can max out PCI-e 2.0 so PCI-e 3.0 is necessary to get everything you can from your GPU, but that day isn't here yet.
Just remember to put the card in the "x16" slot on your motherboard as there are 2 on the GA-970A-D3. One is x16, the other is x4 and that would likely affect your performance some. The slots closer to the CPU socket are usually the ones with more lanes connected to them.