If it was me I'd think hard about what kind of riding would predominate. I have a 29er and an LHT. They both use the same rims, so there is some overlap. The 29er is beefier and heavier because its intended use is off-road touring. I'm riding the Great Divide Route this summer. It has a suspension fork and big disk brakes, plus horizontal bars and Rapidfire shifters. The gearing is very low.
My LHT is for road touring, carrying a load. It has stout tubing (stouter and heavier than my Allez), braze-ons for front and rear racks, fenders, three water bottles, and spare spokes. It can take very wide tires, but not as wide as the 29er. The gearing is also low, but not quite as low as the 29er, and the high gear is a bit higher.
If I could only have one bike it would have to be a compromise. If I was going to be doing a lot of off-road riding, or taking a tour on the Great Divide, I'd go with something strong, like a 29er (and I'd at least have suspension in front, though lots of people say something with a rigid fork, like the Salsa Fargo, is perfect for this route.) It would have knobby tires and disk brakes. If I was spending just a little time on pavement I'd ride it the way it is (like I'll be doing this summer - 10% of the Great Divide Route is supposed to be on pavement.) If I was spending lots of time on the road (like taking a tour on the road) I'd put road tires on it.
If I knew I was going to be riding mostly on pavement, including loaded touring, and occasionally off road, I'd go with the LHT. I'd use wide road tires (32?) for comfort and occasional forays off-road. If I was going to do a ride mostly off-road I'd get really wide tires - probably as wide as the LHT could handle - this is assuming that after the ride I'd be back on pavement predominately.
If you can't afford multiple bikes, at least you can afford multiple tires, right?