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

In any subwoofer output, how important is the Watt output versus the woofer size? I have been reading reviews on some subs such as Earthquake, Sunfire and JL audio. The Earthquakes (15" woofers; ~650W) have reportedly more "slam" than the Sunfire (1000W-1500W, 12" woofer), or the 650W-750W SVS, or even the fathoms.
And each of these are box subs.
Or is it really about the proprietary technology unique to every sub?
In other words, what really influences a sub's output for all the wonderful things we want in a great sub?