|Since both cases have the PSU mounted at the bottom, they both suck for cooling.|
The Problem of Bottom-Mounted Power
I dug up the specs on the Corsair 600W. It's definitely better than the Cooler Master, so I doubt it's the problem (unless you got a bad one).
My guess is you reassembled things incorrectly inside the new case. There was no reason to remove the heatsink/fan, CPU or RAM from the board, did you? And you should have benchtested the board w/new PSU before installing everything in the new case, & then tested it again after it was installed in the case. And the case test should have been performed before installing the HDD, optical drive, PCI/PCIe cards (except video), etc.
I have no idea what your old PSU fan sounded like so it's difficult to make a call, but it seems to me all you needed to do was swap PSUs. By swapping cases, all you did was waste your money & cause yourself grief.