As mentioned a new power supply wont increase ur frames, but its give u room to overclock both the cpu and gpu, which there saying the cpu overclock will increase ur framerate in return, while giving u room with the power supply not getting to its max wattage like u would have with an overclock with ur 500watt.
my 1055t with a 400mhz overclock and R6770 HD barely ran on a cheap 500watt raidmax psu(It ran i didnt trust it running for long). so i got a Corsair GS700 to be safe and run crossfire as soon as i replace my motherboard, i mean with 700watts at the momment its overkill as my 6770 uses half the power as ur 7970. psu recommendation would be a corsair 750watt cx/tx, a ocz fatality, rosewill capstone, or xfx, all usually modular bronze certified or higher and $90-120
For comparision my friend runs a 670gtx with his 1090t with no overclock and his frames are nothing to get upset at lol thats in bf3 @1080p dont remember exact frames but def close to 670 benchmark charts