Never played w/ xf1 or lx7 but owned lx3. The rx100 replaced my lx3. The biggest advantage of the LX series after the lx3.
- optional evf
Biggest advantage against the rx100 for the lx7
- starts at 24 equiv and the evf
If u normally shoot under iso 400, any of the cameras u are looking at are really good, unless u are a pixel peeper, which I am not so take what I say with grain of salt.
Size does matter, both the lx7 and xf1 have smaller sensors which means noise related SW algo's kick in sooner.. The rx100 uses a so called 1inch sensor (really not 1 inch) but twice the size of the other cameras. Dynamic range tends to be better. 20mp is spread across a 1 inch sensor, basically equiv to 10 mp sensor x2. iso 800 no problem. Iso 1600 still looks acceptable, but not as sharp due to noise algo SW. Still better than the other two cameras. Rx100 will be sharper especially at higher iso...
If u need movie capability, Sony video implementation best of the three.
Most pocketable goes to xf1 followed by rx100. Don't like to hold out in front of u, then lx5 or 7 wins dues to optional evf. Need wider than 28, LX series wins. Under iso 400, they are all good.
I am not afraid to pair the rx100 up w/ any camera or use it as my only camera for that matter.
All cameras have their issues, it is a matter of deciding what u an live with. It is late already here, I cannot remember off the top of my head what the blemishes are... I am sure others will jump in..
LCD on Sony the best I gave ever used even in bright sun light.
Good luck w/ your search.