Sub output: Is it the woofer size or the rated RMS

the ability of the cone to stop quickly when the input signal stops?

That would be system Q or damping. An overdamped design would be extremely inefficient (low SPL output at 20 Hz) with a small woofer in a small box.

Compare a WAF friendly product with an ugly DIY brute. (Source HT Shack subwoofer tests)

Both probably sound equally as good but the brute is going to play a whole lot louder cleanly and effortlessly.

Interesting debate. IMHO, there is no question that a larger well built subwoofer will sound better than than ten small cheap ones sharing a box. The issue is that the single large woofer may cost up to $2K! Most high quality 15" subs are expensive and most will use 3 or 4 inch voice coils - not your regular 1 inch VC found in most WAF friendly speakers. This all makes the amplifiers tough job as easy as possible which is what it is all about ....effortless clean dynamic sound with little or no compression is generally why a single large driver matched to an amplifier works well.

I do agree that 10 inch woofers with a whizzer cone tend to work well for a bass player (as in Zu) because there is a slap sound to the bass which is up around 3 to 5 K HZ. But this is not a valid reason to say that a 10 inch for a subwoofer is ideal. Certainly a 10" sub is likely far better than a 6 inch but likewise a 15" will be a lot better than a 10" (assuming good quality in both drivers).

IMHO, ideal is a super big sealed box with low Q (0.5 or so) and a large woofer. The very large woofer and super big box allow for the very poor efficiency of a low Q design.

It seems to me that a bigger, thicker, heavier cone would have reduced "compliance," if that is the right term, and therefore require a greater degree of damping than a smaller, lighter cone. Why would bass damping be independent of this?

Good point. It is actually quite complicated because designers can also make choices about voice coil diameter, magnet size, VC length and mag gap length etc - to compensate for added cone weight.

However, simply put - the big advantage that a large woofer has over a small one is simply that it moves much less for a given output. Smaller long throw cones with long coil in short mag gap (large Xmax) tend to be less well controlled than larger short throw cones (short coil large mag gap). Another issue is heat - small long voice coils have more trouble getting rid of heat and the amp loses control (as impedance rises). Wiring many small woofers together is also going to dilute the "control" that the amplifier exerts over each woofer.

I'd add that long throw tends to rely on long coils and you get less driver control. The relationship between back EMF and inductance is a factor. Long throw designs of any size (even the TC sounds monster drivers) tend to have less control ("braking" if you will or the ability to stop on a dime and change direction).

I agree with Drew Q is very important. Think of damping like your "storm door" - a Q of around 0.3 - 0.5 will be just like you storm door closing - it is extremely controlled and you get absolutely NOTHING other than the input signal coming out (no extra oscillations and no resonances as everything is damped) Like the storm door it is very inefficient (lots of energy to get little output). If you remove the piston from the storm then it wil flap around inteh wind or oscillate freely - this would be like having a q of 1.1 or higher. A Q of of .7 is flat and a good compromise between a good response and decent SPL output but ultimately for high quality you probably want something highly dampedwith a Q lower than that and in order for this to work at reasonable SPL you meed very large drivers or the SPL is to weak.