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

the cone area will increase 29% per driver or 58% per speaker pair.  all else being equal the larger drivers will be capable of more impactful and deeper bass.   this is a significant plus.  
however a larger cone will lower the frequency at which the speaker starts beaming, or become directional.  
this will drive compromises in the design to maintain driver to driver coherence and dispersion, usually a lower crossover frequency and a more expensive, capable tweeter.  
the best sounding most coherent speakers i have heard use smaller woofers, e.g. a ls3/ 5a type monitor that can sound spooky good.  

Bass driver size depends on the design of the cabinet and the driver design to utilize that drivers best potential.  In other words the components and cabinet they are mounted need to  be designed together with an intended sound.
The difference between a 6" woofer and a 6.5" or 8"  woofer wont matter.  The design specification of the woofer matters.  You can have a 6" woofer that has a usable frequency range of 30hz to 5000hz  and a woofer of 6.5" with a usable frequency range of 80hz to 5000hz.  Just because the woofer is larger does not mean it will have as good of dynamics as a better designed woofer.  Either woofer in the wrong cabinet will sound crummy.  A cheap $20 Woofer matched in the right cabinet  will sound better that an $80 woofer in the wrong cabinet.  All depends on the design and quality of materials. not size. Let your ears tell you what is best.

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.