Will this work with my pc and which of the two graphics card has better performance?

G

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they wouldn't work unless you got a better Power Supply that has at least 600W output and a 6 pin and 8 pin PCIe power connectors.
Other than that, the rest of the system looks good
 
Your compter specs have your power supply as a 460w. That is just not enough power to supply a gtx770 and the rest of your computer enough power. If you want to run a graphics card as powerful as the gtx770 your going to need at least a 550w-600w power supply and for a quality unit your going to have to spend between $50-65 for that.

Out of the two you have chosen, the evga is a 2gb vram while the gigabyte is a 4gb vram model. 4gb is unnecessary unless your going to be running two graphics cards or your going to be gaming on a 1440p or higher monitor. For 1080p gaming the 2gb evga model is about perfect.

But you will need a new quality power supply.