In reply to EuanM:
It's important to look at the sensor size of the camera.
Sony RX100 has a 1" sensor.
Panasonic LX100 has a 4/3 sensor.
Both of these sensors are significantly bigger than normal compact which means significantly better low light performance and general image quality.
Also, watch out for cameras with very large zoom ranges (x20, x50 etc.) as these generally have poor image quality (x5 is plenty for climbing/mountaineering).