I'll try to ask a better question.
Is there a commonality among those amps that were among the first to be marketed as MOSFET? I tend to prefer something about their sound that I think of as more harmonically rich and colored, and I would associate with transformers and higher even-order harmonic distortion.
WARNING: Not Class D.

I'm going to try answering this as I find it, not link it with class D amps in any way.
MOSFET's use a 'channel', with Drain on one end, Source on the other, and the Gate applies a charge to pinch off the channel to the point where electrons won't flow through it. It's much closer to the action of the Plate electrode between Anode and Cathode in a valve. It allowed a closer approach to valve circuit topology than bipolar transistors did. Circuits could be much simpler while getting a cleaner output than many bipolar designs.
They are not the same as valves though, it's unlikely they'd sound like overdriven valves, though any nonlinearities in saturation may affect high level output sound in the case where gate charges opened, rather than closed, the channel (look up 'depletion' vs 'enhancement' mode MOSFET's for info on that detail..) It might be like a soft clipping effect.
I have no idea if MOSFET's in a linear circuit with feedback could produce valve-like harmonic byproducts, but if it's down to the topology rather than the semiconductor behaviour, then maybe it could.
Just bear in mind that you may not be hearing what you think. If placebo effect did not work, marketing probably wouldn't work nearly as well as it does.
I developed techniques in phase modulation synthesis that can sound like tape and valve saturation, but have nothing at all to do with the same mechanics. Ears will hear, and the brain will fill in the gaps and then the mind may believe whatever it hears. If it were not so, the synthesiser would never have been invented.
The easiest way to eliminate possible illusions is blind tests, 'ABX' comparison listening tests. It's amazing how those reveal that we often can't tell the difference in sound as well as we think we can.
Ok, ONE link to the Class D amps: It is fast and easy to go between channel fully open, and channel fully pinched off, so instead of dividing voltage in systems that use feedback to control the linearity, the MOSFET is purely used as a switch, dividing time. For this reason, the notion of tone is void, it not quantitative, the QUALITY that we call tone does not exist in the output stage of Class D, unless the timing itself is distorted.
EDIT:
MOSFET's are used as switches because they can be considered like voltage controlled resistances, some of them have resistances that vary from megohms to well below an ohm, so unlike the 0.6V drop across a bipolar junction, a MOSFET is extremely efficient as a switch. They are chosen for this, not for tone.