I come from a computer background and over 25+ years have found that there is not much difference in the different brands of power supplies. The biggest difference is the quality of the internal regulators. For doing the replacement for a Williams 40x it is more out the output rating on the 5VDC and +12VDC. You need a larger power supply that provides at least 15A on the 12V and 20A on the 5V.
I have used both Cooler Master and ThermalTake. I have had good luck with the ThermalTake Toughpower GX1 700 Watt. It has 22 amps on the 5 volt and 58 amps on the 12 volt and has more power than needed to replace both the upper and lower power supplies on the Dotmation machines. This may be over kill, but has worked well for me is 3 machines.
No mater what ATX power supply you get, make sure that it has and internal fan for the power supply.
I have put the ATX power supply in the back right (behind the coin hopper) one and put the other two in the upper cabinet and extended the wire down to the lower cabinet.