$320 would definitely be within my spending range. Would I be getting a significant performance boost, as far as gaming performance?
No. To put in perspective, take http://www.anandtech.com/bench/product/829?vs=858
and double the score for the 560 Ti and that's your comparison (roughly)
I should have clarified. Since your budget was $300, I thought upgrading to the 770 (as opposed to the 760), along with LatiosXT's suggestion of keeping one 560 Ti as a CUDA accelerator, would be preferable. You can sell the second 560 Ti to defray some of the cost of the new 770.
Just a suggestion.
Hope this helps.