The watts of a 20-watt Class-D pocket-sized amp and a 20-watt tube amplifier are the same, BUTTTTT the way the two amps operate and distort are different. Linear amplifiers like a Class-D amp, for instance, amplify 20hz to 20khz in pretty much linear fashion, which means that they amplify more bandwidth; leading to distortion and reduced headroom sooner than perhaps a less linear amplifier. The less bandwidth an amplifier amplifies, the more apparent level it may have over that limited bandwidth. The analogy would be 20 watts worth of power from 20hz to 20khz vs. 20 watts of power only amplifying a 1khz sine wave. The 20 watts of 1khz sine wave will beam a hole in your head so fast you didn't even hear it first. Then there is the nature of the distortion. Digital distortion is not good sounding, so when you hear it, it is obvious. Tube distortion is subtle, sweet, and enjoyable, so when you hear it, you are not as annoyed, which means you will allow a much higher level of distortion before you say yuck, that sounds bad now. The wattage dissipation is the same between the two amps, but one is held to a higher level of scrutiny and is working a little harder to amplify the signal you are sending it, reducing some of the headroom and ultimately lowering the apparent volume.
Even if the amps had a difference in wattage that was off by half ( a 20-watt vs. a 10-watt amp ) the volume difference would only be 3db. That is not enough to really say one is considerably louder than the other. Certainly not enough to make one be able to go over the drums and the other unable to go over the drums. It all comes down to perceived level and accepted levels of distortion. When you hear bad distortion your stop, when you hear good distortion you keep going. Digital Class-D amps have bad sounding distortion vs. that of tube amps. But if the two amps are rated at 20 watts, both will produce at least 20 watts ( or at least they should ). A few watts is + or - is not enough to make or break either one.
