Not at all in my extensive experience.
If the speaker parameters were to change enough that the characteristics of the speaker became that different, it would actually be indicating that there is an ongoing and continuing deterioration of the speaker.
Most speakers are designed for stability over many thousands of hours, and while a very small change may occur, it's rarely audible (though can be measured through the electro-mechanical parameters of the speaker before and after).
I have tested many speakers specifically for this attribute, this is one way to determine the short and long term mechanical power handling of a driver... by TS parameter shifts.
Yeah, this is still a very live topic of debate. Eminence Speakers' tech blog says
speaker break-in is no myth, but that's the only source of real authority on the topic that I can find still espousing that conclusion. Every other credentialed expert I've heard or read, and almost every other objective test, however rigorous, that I've seen done on speakers ranging from a few hundred to several thousand dollars, all agree with you; any difference, if not measurement noise, is imperceptible to human ears (less than a dB, the same standard used to match pairs).
Taking it easy on your speakers for the first few hours, and/or playing full-range sound recordings or pink noise through them, certainly won't hurt the speakers, but with one notable exception, the consensus is it's a waste of time.
So, that leaves us with the OP; a 2014 Markbass CMD102P and a 2020 CMD102P have significantly different volume and tone at identical settings. Why this happened is still open to discussion, and over a 6 year timespan involving moving production halfway around the world and making perhaps hundreds of thousands of these amps in the meantime, there are a
lot of possible variables. However, the biggest one is the assumption that identical positions of the knobs are actually identical settings. Deviations from ideal spec in the gain potentiometers alone could explain volume differences like this.
That's why people who build these circuits, like pedal manufacturers trying to recreate vintage amps or effects pedals, don't do shootout-style tests with knobs in identical positions. That's a good start, but then they will tweak the controls until a single common point of measurement (i.e. a reference mic or dB meter) indicates both units actually are behaving identically (or as close as possible), before subjecting both of them to human ears. The eagle-eyed YouTube viewer then points out they aren't set identically so it's not a fair comparison, when in reality two vintage units, even with adjacent serial numbers, could require the same difference in settings to actually sound the same. If manufacturing tolerances were close enough that
identical settings produced
identical sounds between
any two units, you'd be paying $2,000 for a Tubescreamer. The number of situations in which even having matched pairs of equipment actually makes a perceptible difference are very few, especially outside the recording studio.
In summary, turn up the 2020 amp's master volume or gain above where the 2014's is set. If you can get the same measured volume without clipping as the 2014, just at a higher setting on the dial, chalk it up to variances from ideal spec in some major component or two that determines actual preamp gain or master volume. Over 6 years, you
might note an explicit spec revision designed to increase longevity at the cost of efficiency or maximum gain, but you'd likely need access to Markbass's internal R&D communications over 6 years to find it.
In bocca al lupo.