Just ordered a new PSU to solve a problem, want to hear your thoughts

Before we get to the specs, here's a little background. I just put this cpu and motherboard in my system. Before I was using an old AM2 board with a phenom II x4 955 and I was having no crashes with all the same hardware. After putting in the new cpu/mobo combo, my computer shuts off abruptly when playing more demanding games. Counter strike source and BC2 work fine as long as there isn't too much going on in the background. All the games I have run amazing, GTAV works for a minute or so and the computer shuts off and reboots, but it's buttery smooth and my temps are fine while it's working. I believe I've narrowed it down to the PSU, so I'm just wondering if anyone else has had a similar problem. Here are my specs.

CPU: i7 3930k

Mobo: ASUS P9X79 WS

Ram: 4x 2gb ddr3 1333

Video card: Radeon R9 280

HDD's: 1x Sandisk 240gb ssd, 1x WD 7.2k, 1x WD 5.4k

I just ordered a 600w corsair power supply to power this system. Currently I'm using unknown brand 750w psu that (I believe) is the reason my computer shuts down and reboots when gaming. I have two questions.

Is this enough power for this build? PSU calculators have told me anywhere from 513w to 730w is recommended.

Could my current PSU be running a lower wattage than is required to fully load my system and would that cause the crash I've described?