The RX100 definitely has a sensor to die for and if you like the rest of the camera they built around it and want to spend the money, it's a great little camera. I had one that's my wife's now and she leaves it on auto and loves it. But to get that big a sensor in such a small camera, the lens is pretty compromised in terms of both aperture (which I care about) and corner softness (which I don't). And the handling, to ME, is terrible. I just couldn't enjoy shooting with that camera.
The LX7 sensor isn't in the same league, but the lens is really nice. The sensor is only good up to 400-800 and maybe useable to 1600 in a pinch, (the Sony is good at 3200) but you can do a LOT with that at f1.4 - 2.3. And the multi-aspect sensor and all of the external controls make it waaaaay too much fun to shoot with. I'm hopeful they'll do a good 1" sensor compact within the next year or so, but to maintain a sharp and fast lens they're gonna have to make it bigger than Sony did and bigger than the LX7 - maybe X100 size? Or maybe they'll compromise on the lens too and keep it smallish? Hopefully the trade offs will work out. Meanwhile the trade offs on the LX7 work way better for me and at that price, it was an easy call. I suspect we'll look back at the LX3-7 as classics of their era. I'm loving the LX7 again - it was hard to justify at full price,given its obvious limitations compared to the RX100 and X10, but at $300 or less, I couldn't pass it up. Ita one of the most capable and enjoyable all around cameras I've ever shot with.
-Ray