Big difference is stability
The difference you'll have is in whitewatering and also being able to take an extra person. With an 11' boat you'll have more of a footprint in the water, giving better stability through a whitewater run. Basically the same as if you go 4x4ing with a jeep vs a suburban. A jeep can manuever quicker, but bounces around alot more, expecially through the rough areas. Whereas the suburban may not handle the quickest, you glide a bit more over rough terrain.
I'd say go with the bigger boat. Personally speaking, a 12' boat is the perfect all around one man boat. If you actually sit in one, and look at it, they're really not that big. If you go with a single fishing frame, you really aren't overkilling the boat. Plus, you can add a small passenger frame, and now you have a two man boat as well. I'm in the process of custom designed a 2 man frame for a 12' set of tubes.
So, what kind of boat are you looking at? How much do you want to spend? Really dictates on what you can get. I know I normally custom build all of mine (I buy the tubes then I have a frame builder who does the welding work on my designs). You have alot of options. I'll say this, before anyone goes out and buys an outcast/bucks 2man boat. Speak to me. I do preach Steelheaders, but can also put you into other whitewater tubes and a frame builder. Just that a Steelheader is ready to go, and really not that much more expensive then the Buck's/Outcasts I've seen. Plus he's in the PNW, and has a good guarantee. I do believe his 12' boats are going for about $2100, give or take, which is comparable to the bucks (and holds almost 800#'s more weight).
Good luck. Let us know what you end up getting. But, if you're interested in the custom route, let me know.
"Good angling ethic is not a monopoly practiced just by fly fisherman" - Bill McMillan