Bass Driver Size - how much better is an extra inch?

Just look at speaker manufacturers.  As you move up the line they get bigger... Most flagship models within a speaker line are there largest.

I do believe though that you can overpower a room with speakers to large for that room but the room needs to be small, like my 11x13 room, and the speakers have to be rather large.

Don't confuse frequency response with impulse response (impact) in regards to low frequency drivers. While a well designed 6.5" driver can cycle quite low in a well designed cabinet, it will only have a fraction of  the impulse response of a larger driver. Not all music styles require impulse response, like folk music or traditional jazz to name a couple, but impulse response is a major part of most modern music created since the early seventies and you will not get the full effect of that music out of a small speaker.

One way to get the transient response of a six or eight inch woofer out of a fifteen inch woofer is to put an appropriate fifteen in a well designed corner horn.  Admittedly this mandates a largish enclosure.  Mine are 18 cu.ft. each.

I have a 16' x 15' room with a pair of Klipsch K-horns in the corners of the long dimension (they're 1978 models that have an updated (per spec) crossover and modern wiring (lamp cord was original).
I've often wondered if I would significantly improve the sound by adding a subwoofer?

Emergingsoul wrote: 

"Have older b&w speakers and bass drivers are 7 inches vs 804 d3 speakers that are 6 1/2.  The larger drivers seem to really open the sound stage, more open and less constrained.  Imaging of older speakers not as good but a very enjoyable listen." 

Imo the difference between 6.5" diameter and 7" diameter drivers is inconsequential. 

I think you are SEEING a cone size difference and HEARING a sonic difference, assuming that the one is the cause of the other. 

My guess is that there are other factors involved which are not readily apparent, but which have a greater effect than the small difference in cone diameter. 
 
Duke