RX1 or RX100 Backpacking the World.

If you want a versatile recorder of your wordly exploits I would suggest the Rx100 - you will save a bundle which you can tuck away should you need extra funds along the way.
HGowever, coming out of left field now, I would actually suggest neither of your options (and that's me who is traveling with a Leica M9 and the RX100 these days, among other gear). Rather, consider the weathersealed, smallish, rugged, solid Pentax K5 with a couple of equally weathersealed, smallish, rugged and solid primes which Pentax is so well known for. There are very inexpensive deals on this camera now, and it's been the top rated (or thereabouts) APS-C camera on the market for a while. You can beat this camera up in all climates and under all circumstances, it probably won't let you down. Then add the Samsung EXF2 for a casual and pocketable alternative. It's "only" 12MP, but it has an extremely fast f1.4 Rodenstock lens and a (quite) useful zoom range, too. The AMOLED swivel screen is one of the nicest out there. PLUS, it has build-in wifi, so you can just beam up your files to anywhere you want for cloud storage. I have the EXF1, and still use it quite a bit, it's a very well build little camera, heavy, but still pocketable, and totally underrated. Very sharp lens, works well as a JPG-only shooter, too. Just my two cents...
Happy trails!
(P.S.: If you're not already, traveling the world a lot will convert you to being a pragmatist, I can assure you)