Keep the RX100 and buy the A6000.
I recently purchased the A6000. It's been on two backpacking trips with me, one of which we saw plenty of rain. I've come to prefer the 16mm Sony lens and I don't think I'll bring the 16-55mm on another trip since 99% of my shots are wide angle. From reading the reviews, I thought I was supposed to hate this lens but I guess I'm not sophisticated enough to know better. It's been great for me and my next purchase will be the fish eye adapter for it.
So for backpacking, the only thing missing at this point is a zoom lens for wildlife. At one point, I considered buying a Sony 55-210mm for this purpose but I've decided to go another direction and buy the Lumix ZS-25 for a several reasons:
1. Around town, and when traveling, I like having a camera with me but don't always want one hanging around my neck screaming "I'm a tourist!" Even with the 16mm lens, the A6000 is only pocketable in a jacket so I'm left either carrying it around my neck or carrying a camera case when I'm in jeans and a t shirt.
2. The Lumix has a 24-480mm (35mm equivalent) f/3.3-6.4 Leica lens so this gives me a greater range than the Sony 55-210 F4.5-6.3 (82.5-315mm equivalent).
3. The Lumix with battery is half the weight of the Sony 55-210 lens and less bulky to carry on my person when hiking.
4. During a rain storm, I feel more comfortable working with a point and shoot than the A6000. Much of this due to the fact that I'm not rich and it's easier for me to replace a $150 camera than a $800 camera and lens.
5. If my A6000 ever decides to $#!+ the bed when I'm backpacking, I have a capable backup camera.
6. It's half the cost of the 55-210mm lens.
My dad owns the Lumix ZS-25 and it's his go-to camera for traveling. I've had an opportunity to play with it and check out his photos; I've been nothing but impressed and thinks it’s a great value at $150. The only "con" I'd give it is the lack of view finder which I find invaluable on my A6000 and use 90% of the time even though it uses more juice than the screen.
From playing around with a couple NEX cameras, I'm glad I went with the A6000 and have no regrets. I will mention that the video overheating issue persists with the A6000 and had that happen to me in Seattle last week after 15 minutes of recording. There was a heat wave (by Seattle’s standards) last week which may have contributed but whatever improvements they’ve made to the heat sink have been insufficient (anecdotally) for this to compete against other cameras video. That isn’t a problem for me since most of my video recording is limited to a few minutes here and there but ymmv.