I have a EVGA GeForce 560 ti 2GB, and I'm thinking of upgrading to Gigabyte Radeon 7950 3GB?

That's a great jump in gaming performance since the HD7950 is significantly faster than the GTX 560 ti:

GTX 560 ti VS HD7950 gaming benchmark:

http://www.anandtech.com/bench/Product/547?vs=550

560 Ti Upgrade

in case you could cope with to pay for it, the GTX 670. The Radeon HD 7950 if strictly identifying on between the $300ish taking part in cards. Fdasf what are you smoking? The Radeon HD 7870 Ghz version beats the GeForce GTX 660 (non-Ti) in maximum video games, yet is slower than a GTX 660 in BF3 and Crysis 3. however the HD 7870 would not beat a GTX 660 Ti in any state of affairs. the hot Radeon HD 7870 LE (i.e. the 7930) beats the GTX 660 Ti, yet it quite is a thoroughly diverse card.

There is a huge difference between the two. You can definatly see a difference between the two. Personally i would get a Sapphire radeon 7870 XT.

The XT model has the same gpu as the 7950. Its definalty worth it. And its way cheaper than the 7950. The XT is 260.

there's a huge difference. the 560 TI is a mid-high range nvidia card from the last series and the 7950 is one of the best that AMD has at the moment. if you want to, go for it.