RX1 or RX100 Backpacking the World.

I'd take the RX100.

• I could buy 5 (nearly 6 actually) RX100s for the price of the RX1. So you could actually buy two (one for backup) and still save a small fortune over the RX1. What could you buy with the savings ?
• Size & weight. The RX100 is significantly smaller, lighter.
  
• At low ISO (whenever there is good light) There is little advantage to the larger sensor. Most of the images you take from the RX100 therefor will be as good as you would get from any camera, or close enough. You could make saleable images with this camera. Its not too bad at higher ISOs either.
• The flexibility of the zoom is a significant asset. The wide end will provide more scope for landscape images, the long end for portraits of people. In between you have focal lengths to suite a variety of subjects and cover any events you might be attending. Backpacking the world, you will use your feet quite enough, without having to zoom with them on every occasion. This flexibility might enable you to get shots just not possible with the RX1.

Regards

John