The size of the driver is just one specification that you need to consider. Power handling, voicing, and crossover type will affect the performance.
As an example, I have a pair of first generation JBL Eon PA speakers that use fifteen inch drivers. I also have a JBL Prosumer ten inch powered subwoofer. Neither product could be called esoteric, or super high performance. The bass produced by the Eons when pushed is really lacking. The little ten inch sub on the other hand can make the house shake to where you would think Godzilla was stomping on the roof..
So to answer your question, Yes... a dedicated subwoofer will probably generate more bass energy, than a set of stereo speakers. This will be especially true if the stereo speakers utilize a passive crossover. This doesn't mean you will achieve better overall sound. There will undoubtedly be an overlap of frequencies between the full range speakers and the sub which will tend to muddy up the lows. A proper Sub/Satellite system should be designed to work together.