I was looking at giving my brother my old palit 580, but he only has a 600watt power supply, would it run battlefield 4 and crysis 3 without problems?
The PSU in question:
It has the minimum wattage, which is 600watt but also has 48amp on the 12v rail which is more than its minimum requirements.
You shouldn't have any problems running a 580 on a 600w power supply - that Corsair has enough headroom for pretty much any single-GPU setup. He'll be able to run both of those smoothly at excellent graphics levels.