(NOTE - in this post assume that WATTAGEs are compatible / appropriate.)
Previously I had thought that you identify compatibility of PSU's (in a particular PC) by their associated form factor, e.g. "ATX", vs "Mini-ATX".
But today I brought an ATX power supply to replace an ATX power supply on an HP Pavilion, and I could not, because the Pavilion has a very small power supply, about half the size of the one I brought (so there was not room inside the PC for my bigger PSU)
LIkewise, in a different situation, I was unable to use an old ATX power supply from a P2 or P3 in a newer P4 motherboard because it lacked the "P4 ATX" connector, for the CPU power.
And in a third situation, an ATX DELL PC had the external power cord connector on the opposite side, so if you tried to use a regular old ATX psu, the power connector was was blocked by part of the case, as I remember.
So obviously, just because two PSU's say "ATX" doesn't mean they're compatible. (They don't necessarily fit into the same PC).
Are there just too many variations of PSUs WITHIN the ATX category to be able to generalize? When you are replacing a CPU, do you go by the PC MODEL NUMBER, and check compatibility of PSUs on the web FOR that model #, rather that go by form factor?