I've owned both and... overall... I would recommend a raft. Primarily because you seem to be asking for something to 'do it all'. But I fully agree with other comments on this thread: it can depend in large part on the waters you plan on floating.
I owned a 14' raft self-bailier with a flyfishing frame and loved it. They are very stable. Me, my buddy, and my Labrador could all lean over the edge and feel completely solid. You won't get that with a drift boat. Also, a raft can float in very skinny water, which you will find in the fall/winter. You just glide over rocks that in a drifter you'll bash and have you reaching for something to steady yourself. You can also pack a lot more gear, so that gives you more multi-night camping options (think Smith River).
The drift boat I owned was a 16' fiberglass Clackacraft. And drift boats are great if your primary purpose is fishing, no doubt. They are much more maneuverable and even with decent current, you can 'hold' in place. I also found them to be lower maintenance, especially with a cover. And many can be fitted with a motor, as mentioned, which saves you from having to deal with a shuttle. Which, again, depending on your circumstances, can be a huge logistical hassle.
If you go driftboat, I would not recommend a wooden driftboat, no matter how pretty they can look. Too high maintenance and if you're in whitewater or even just a standard MT trout stream, they're going to get beat up. In the late 90's when I lived in Missoula, everything I saw was fiberglass. When I moved to Idaho in 2002, all I saw was aluminum. Aluminum boats are, generally, almost bombproof. But, any nicks on the chimes and you really gotta watch your fishing leader. And they're cold and noisy as hell in winter. I'd go fiberglass.
Hope this helps.