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

"All the wonderful things we want in a great sub". First, if all you want is lots or rumbling that can destroy your walls (and ears), any cheap sub with 10,000 watts can do it. If you want accuracy, the wattage is not nearly as important. If you want truth, then the wattage depends on what type of music you are trying to reproduce.
Are you looking for a sub to double as a "movie sub", or just for music? And is that music Hard rock/heavy metal? or Jazz and classical?
Hard Rock and heavy metal just needs lots of power. Jazz and classical need finess.
So we all do not need the same thing from a sub.

A large driver in a large cabinet needs less power to produce deep bass. A small driver in a small cabinet must have huge amounts of power and much further excursion to produce deep bass. A small driver may seem like it would produce faster bass but in reality it must move further than a large woofer to output the same amount of bass. The laws of physics are constant and unchanging.

Elizabeth hit it right on the head and Rwwear went a step further.

But the small cone has more linearity in its movement. It is fascinating to see the large driver/small driver debate return again after we all thought it was settled. When I was young the bigger the better was the rule, EV had a 30" woofer, Hartley a 24". In music reproduction the last 40 years has seen a gradual reduction in driver size. This may or may not apply to HT. But the driver size or amp power alone tells you little about the quality of a particular sub, a good designer can use either paradigm. You have to match the performance of a particular unit with your requirements.

"But the small cone has more linearity in its movement"

Huh?....smaller drivers are made, so that you can use smaller boxes, so that the buyers wife will be happy, or at least, more happy than she would have been with larger boxes in her living room....(no other reason for doing it, purely marketing).

Dave