I've read that 12" is xx% more light gathering than the 10", maybe it's that 44% that Graeme suggested above, so obviously it makes a difference..
How much difference when you're at the eyepiece, will be up to the individual I suppose as everyone's experience may be a bit different.
But you do have to think seriously about portability - not only is the 12" a bigger and heavier mirror, the OTA is longer and bigger, the base is bigger and heavier, and of course, the cost is more.
My 10" is just on the side of portable for one person, I wouldn't want it too much bigger if I still wanted to be able to transport it in and out of the house by myself, or try and put it in the car.. the longer OTA and bigger base of a 12" just wouldn't fit in my car.
So you need to take all that into consideration, not just what extra faint fuzzy you might see in the 12"