There is not just 1 difference, there are many.
Small speaker tend to sound more direct.
Small speaker tend to have a frequency response that goes higher than large speakers.
4 small speaker can take more power than one large speaker.
Small speakers act faster than large speaker.
It's really a taste thing. My bass cab has 2x10'' speaker, and I'm very happy with them.
I prefer a 4x10 rig vs 2x15. It seems to me that 4x10 gives a tighter, punchier sound that's easier to hear and understand close to the amp than 2x15, which seems to focus way out front. I got rid of my old Sunn Concert 2x15 because I could never really tell how loud I was at gigs in small clubs. It could be a perception-only thing but that's okay: the perception of how one sounds has a direct effect on how one plays.
I'm in the 2x10 school, because of the tight sound, but I do keep a 1x15, in case there's an outdoor gig. Other wise I'll just use a bunch of 2x10s. And lot has to do with which brand of speakers you're using.
It's tough to beat 4-10's for pure cone surface per cab size. All else being equal (although it never quite is ) that equates to more low end efficiency/capacity.
Once I got up to speed on the concept that 10's were not just for high end, the 'bi-amp, 10's on top, 15 on the bottom' stack seems rather silly.
My wife's rig is a 4-10 and a 2-10 that works out to be a nice go-anywhere compromize.