In my experience with both AB & D versions of the Markbass LMII/III, I found the Class D LMIII version did not quite feel as taught/firm under my own fingers vs the older AB LMII/IIIs. My guess is its likely something to do with how the different power sections 'control' the speakers. I especially noticed that the class D LMIII ran out of steam rather quickly when turning up the volume powering an 8ohm cab. However, at 4ohms I found the LMIII to have plenty of power, though it still had a slightly "looser" feel to the sound vs the class AB models. In theory, the preamps of both AB/D LMII/IIIs are the same.
That said, I think the Class D LMIII may actually go a bit "louder" (but perhaps with less definition) than the AB LMII/III at 4 ohms. It seems that is where the Class D LMIII is at its strongest, with the most headroom. Just my observations...I still prefer the older AB LMII/III, as the sound comes across as a bit thicker/denser, less wide/clinical, to my ears. Also note, my observations are very specific to the LMII/III series, and the implementation of Class D in this particular model. Markbass also designs their own power modules unique to the industry standard ICE modules. Of course, any one amp, of any amplifier class, should be evaluated based on its own design merits & user experience. For example, the 800 watt module used in the current LMT800 seems to have quite a bit more clean headroom than the current LMIII at 8ohms.
Ive played many different lead sled and micro amps, and feel design/implementation can make a world of difference. Heavier does not always equal louder, smoother, or more defined bass either. Ive played a few "lead sleds" that didn't quite deliver upon expectation. However, the best of the AB amps Ive played certainly had plenty of headroom, presence, and definition that is very compelling. Overall, modern Class D modules- and more importantly, how they are implemented- continue to improve to the benefit of many bass players. But, I think its important to choose amps based on one's own ears and experience, rather than just looking at the specs.