[Hugh Haynie]"Will an AMD Radeon HD7950 3GB GDDR5 7121A10000G work in a Mac Pro 3.1 tower?"
According to both EveryMac and OWC, the AMD Radeon HD 7950 is not compatible with the Mac Pro 3.1 (2008).
I would go with the ATI Radeon HD 5870 which I have in my 2008 Mac Pro 3.1 8-Core. Honestly, I upgraded my 2010 Mac Pro 5.1 12-Core from an HD 5870 to the AMD Radeon HD 7950 and I really didn't see that much of an improvement. I ran some benchmarks and it did get higher scores but in every day video and graphics work it was not as dramatic as going from an HD 5770 to the 5870 which has twice the power.
Also note that the HD 7950 supports PCI-Express 3.0 which neither the Mac Pro 5.1 nor 3.1 have so it won't run at peak performance anyway. I'm guessing this is why I didn't see a big boost. IMHO, the HD 5870 is a better price performer and a lot cheaper than the HD 7950.