The way you phrased the question was "if you had a choice", well, here's how I'd do it:
I'd throw my KTM 500 in the back of a truck w/a couple of ramps, and take off with a 17'
Casita
Moab, the desert Southwest, Arkansas, etc.
This way I wouldn't have to pack anything but water, tubes, and tools on the bike.
So to me, it really boils down to what kind of riding do you want to be able to do along the way? Paved only? Paved and mild DS? Paved and serious DS? DS only? That kind of dictates a lot in my view.
For me, the setup in Bob's pic would be ideal, but I'd want my KTM 530 EXC and my 1200 GS.
If I were going to do the one bike road trip thing with lots of camping, I'd pack up the 1200 GS and go. A few nights a week, I'd find a decent hotel for showers, a softish bed, and a real toilet. You can spend a LOT of nights in hotels before it adds up to the costs of running some kind of big RV (purchase cost, fuel, maintenance, etc,...). However, by going on one bike you limit your riding opportunities. Also, unless you are comfortable with leaving belongings at a camp side while you are out riding, you have to carry EVERYTHING on you all the time, unless you leave it in a hotel room. There is still the risk of shifty hotel staff messing with things
I've done a few of the camp off the bike trips with the KTM 530. Even with really minimal gear, there is considerable weight added to the bike. When the going gets rough, NOT having that weight is nice. So I like the idea of getting to a place, setting up base camp, then spending time riding in the area carrying only the minimum of tools, tubes, etc... like Bob mentioned. I'd still want the GS though because sometimes it is just nice to do a good long ride on the paved stuff, with maybe some unpaved here and there.
For the length of time you mentioned and since you would be alone, I would be looking for something between minimalist and big in terms of an RV. One of those tiny tear drop trailer things wouldn't cut it. However, I don't need the giant luxury RV either. Something like the trailer shown in Bob's post would be ideal. After all, you might be spending a few days in a row holed up riding out nasty weather and something really small, or a tent, would get old REAL fast!! I used to live in a 38 ft travel trailer in college by myself. It had plenty of space, but even that made me feel a bit stir crazy if I had to be in it more than a few days in a row.