Are you saying that if I have the 30 watt amp hooked up with the .5mv cart and I have a comfort listening level at say 12:00 position on the control, then I switch amps to the 60 watt (with the same .5mv cart), that I will NOT have to turn the volume control down somewhat to achieve the same listening level?
More often that not the answer would be yes, but not necessarily. The effect on volume control setting of changing the power amp would be dependent on the gains, or input sensitivities, of the two power amps, meaning what input voltage is required to drive the amp to its specified output power. Typically a 60W amp could be expected to have higher gain than a 30W amp, but that is by no means always the case.
But the only significance any of that has is that the amp gain should match up with the gain of the rest of the system such that the volume control does not have to be used near the extreme top or extreme bottom of its range.
The fundamental benefit of a 60W amp vs. a 30W amp, everything else being equal, is simply that it will be able to handle louder peaks without clipping.
The major concern with going to a lower cartridge output, again, is that hiss levels do not become excessive. Yes, by staying with the 30W amp you would be turning up the volume control to a higher setting than you presently use for the higher output cartridge, and yes if you were to change to the 60W amp you MIGHT not have to do that (depending on its sensitivity or gain). However, that would be irrelevant to the hiss level -- if the 60W amp has higher gain and greater sensitivity than the 30W amp you would not have to turn up the volume control as far, but at that lower volume control setting you would wind up with the same volume of both music and hiss as you would with the 30W amp at a higher volume control setting.
That is because the hiss level is determined, as I said earlier, by the amount of noise which is generated at the front end of the phono stage (all electronic devices generate some amount of noise, and the noise generated at that point in the system is what is critical because it is amplified by everything that follows). While strictly speaking the critical parameter is the noise performance of the phono stage (which can be defined as "signal-to-noise ratio" or "noise figure" or "equivalent input noise"), with high quality equipment that will correlate with the gain of the phono stage, which is why the others discussed the issue in terms of gain.
Good luck with the new cartridge!