Look at the graph in the likI added:
http://www.dpreview.com/reviews/panasonic-lumix-dmc-lx100
The LX100 has a much bigger sensor so its effective aperture is far faster than the RX100 MK3, by at least 1 stop so it is kind of like comparing an APS-C crop DSLR to a FF DSLR.
the DXO mark overall score may be the same but that is a fairly pointless number, you need to look at the details. The LX100 sensor has a consistently higher dynamic range, by nearly 1 stop iSO400-800. At the higher ISO's Sony cheat and applies noise reduction. At base ISO there is some kind of amplifier noise limiting the LX100.
The RX100 MV4 improved the sensor a little, using new backside-illumination technology. This resulted in about a /3rd of a stop improvement in DR close the gap.
Not huge differences but you get around 1 stop more light and shallower DoF with the LX100 (so like crop vs FF) and 0.5-1.0 stop more DR over certain ISO ranges. The downsidw i the lens and camera are bugger to support the larger sensor, but the camera is also better built with more manual controls as well.
All just depends what you want, the Sony RX100 is smaller but still isn't a shirt pocket camera, the LCX100 is a good bit bigger but is still very much a pocket camera.