Tonally, there is as much variety in 10" drivers as 12" drivers. You won't start to notice a big difference in terms of volume of air moved until you get into 4-driver cabs. A 1x10 and 1x12 can be just as full sounding as a 2x10 or 2x12.
Efficiency will have a noticeable difference on SPLs if you use the same amplifier with the same settings.
But to say "10-inch drivers are brighter and thinner than 12-inch drivers" in this day and age is a fallacy.
One thing you can get with a 10" driver over a 12" driver is speed. Since 10" drivers do move less volume of air, they are generally EQ'd to take advantage of that, and by adding to the low frequency response, they would start to sound slow and bloated.
Also, the cabinet you're using is at least 30% of the equation when it comes to frequency response; I would say the total equation is:
30% Cabinet
30% Driver(s)
20% Amplifier headroom and EQ
20% Room size and placement