The iPhone 6 camera is only slightly better than the iPhone 5S for your purposes. The iPhone 6 has slightly improved speed, image processing and low-light pictures. But only slightly.
That being said, I'm not a professional photographer but I've been taking wilderness photos almost exclusively on smartphones for years now. iPhone 2G, iPhone 3S, iPhone 4, iPhone 4S, iPhone 5C, iPhone 5S, iPhone 6, Galaxy 34A, Galaxy S5 and Nokia Lumia 920.
Of all the newer incarnations, the iPhone 6 is usually my go-to for pictures. The S5 is a close second though.
On a typical trip I bring the iPhone 6, Galaxy S5 and a GoPro Hero3+ Black (yeah, not so UL!) Generally the iPhone 6 runs GPS (Gaia) and I use the S5 for still pics and GoPro for video.
The main disadvantages of using your phone for pictures is that it will drain battery life on a trip, meaning less power for GPS/calls/etc. Smartphones also hit a wall pretty hard when it comes to optical zoom and low-light performance. Don't expect much there.
The great advantage is that you don't need to carry an extra device, batteries, lenses, etc. A phone is reasonably light and you are probably going to bring it with you anyway.
A few tips on smartphone photography:
1. Don't zoom. Just don't do it. If you absolutely have to zoom, keep it to a minimum. Zoom on a smartphone is generally software-driven (it just upscales your photo) and leads to rapid loss in quality. I'd rather get a crisp shot at a distance than a fuzzy closeup.
2. Take multiple shots, always. Smartphones aren't the precision instruments that high-end cameras are. Half of your shots will come out slightly out of focus or with poor exposure, especially since you aren't usually mounting a phone. I always take 3-5 shots at a time so I can later prune out the bad ones.
3. Use a third-party camera app that provides focus and exposure lock. Camera+ is a great app for iPhone with focus/exposure lock and also has exceptional post-processing so you can lay in the tent and play with photos at night. :) Focus lock is great for getting macro shots, and exposure lock is going to be very useful in weird lighting conditions where you need to override the camera's auto exposure.
Anyway, just a few thoughts – good luck with your photo adventures!