In cathode-bias the signal is instantaneously amplified, because the tube does not have to "wake up” from a less than full operational state of fixed-bias. So, it makes for an amp that has a certian tonal-richness at all volumes, as well as, being very touch-responsive.
There is not as much headroom as fixed-bias because of the lower plate voltages used in cathode-bias, so it can be a virtue for players depending on amp output stage overdrive, with smoother transitioning from clean to crunch.
A fixed-bias amp will generally have more headroom and wattage with the same circuit topology, as well as a tighter bass response, all factors due to greater voltage getting to the tubes during conduction.
Essentially. In general that varying voltage (as well as lower voltages in general) is what gives "class A"-type cathode-bias amps such "lively" touch sensitivity and smooth transition into overdrive. That general compression ("squish") has to do with the lower voltages (compared to fixed-bias) going to the tube plates in cathode bias. Higher voltages (i.e. fixed-bias) give an amp more wattage, headroom and bass-response (generally), among other things.