when you're dealing with the most common single stage single ended tube mic amp, everything you do or change is audible. This includes capsule, tube, xfmr, AND PSU's.
In short, topology and implementation matter.
There are a few different B+ reg techniques, and they do sound different from each other.
There are also very expensive vintage mics that get used by pro's everyday that have NO B+ reg.
Remember that your decisions about what psu type to use will have to take into account it's effect on sound, as well as all the usual specs (hum, noise, heater/B+ ramp up, impeadance vs. frequency, shorts capability, cost, size, power draw, field generation). Looking at the specs side only might provide functionality, but not necessarily an ideal sonic signature (please don't get the idea that there's no such thing as a sonic signature- every piece of gear has one by definition).