How much lower is the wattage on the other one? Keep in mind that the one that came with your computer is designed to handle the computer as shipped plus a fair amount of extra cards and drives under heavy load - if all you've added is some extra RAM, I would expect a power supply that is at least 300W to be plenty, at least for testing. Although the CPU in your system is infamous for its power consumption, most normal computers idle at under 100W and rarely go over 200W, add 50W for it being a pentium4 and 50W to that for power supplies degrading over time and some PSU manufacturers being liars. If the PSU is too old it might be designed for the wrong maximum amperage on the different rails to suit your computer, but if it is that old it probably won't have the correct connectors anyway.
Waterdam: it might be a good idea for you to open another thread (although you might want to follow this one) since many different things can cause freezes. Please let us know what computer you have - either the manufacturer + part number or a list of components, along with which version of Windows you're running and a description of when it freezes, and what had changed between the time it ran fine and started freezing.