Ricardo - I'm jealous of your location ;-) Very pretty, great light.
When I bought my LX7 I also considered the RX100. Overall I preferred the ergonomics of the LX7, I found it much easier to hold the LX7 steady, compared with the RX100, which I found quite slippery. My previous p&s was a LX3, apart from the poor battery life (tired batteries), it's still going strong.
Compared to my LX3.
Much quicker focus, even in poor light. Less shutter lag.
High(er) ISO noise is significantly lower, 1 may be 1.5 stops
Lens is great, nice contrast, great colours.
Longer at the tele end.
Many more art modes.
Better LCD screen, in terms of colour fidelity and contrast in sunlight.
Image stabilisation seems to be better.
Video is much better quality and you can zoom whilst filming !
Don't like the noise reduction, can be intrusive under some circumstances.
I love the results at the macro level, not macro as in tiny details, but the overall look and feel - the big picture. For the RX100, the micro detail is there, but I think it looses out a little when looking at big picture.