I think to prevent this staying off topic, I've done a little research. I don’t normally look at things this closely but this is as accurately as I can put it.
I'm unable to find RAW samples from the RX100 II in comparison to the LX7 so the closest I can find are from the mark I vs LX7.
http://www.dpreview.com/reviews/panasonic-lumix-dmc-lx7/11
Here we can see the RAW output of both. Using LX7 ISO 400 and RX100 ISO 1600 again for comparison, unfortunately the settings are all over the shop:
LX7 - f4.5 @ 1/160 vs RX100 - f11 @ 1/200.
If you care to do the calculations, you'll again see the RX100 should be at 1/250 but its close enough (1/3 stop). Here the DOF is evened out too.
I’m using LR4 for my conversions and comparison.
In LR, the histograms are similar enough to say they are equally exposed, but the actual image composition is slightly different.
To my eyes the images are similar with more chroma noise in the RX100 sample but more luminance noise in the LX7. The differences are small enough such that I'll just say the RX100 at 1600 is about an LX7 at 400.
BUT, there's an impressive amount of detail in the RX100, more than that of the LX7. So the RX100 is keeping the 2 stop advantage despite having a fair bit more pixels. With only modest NR the RX100 starts to better the LX7.
The mark II's sensor is slightly better than the mark I so we can extrapolate that the RX 100 II moves the bar ahead even more, noise wise.
The scene doesn’t really stretch the DR all that much but in these DR seem comparable.
What about the overstated ISO settings. Well it turns out they both do it.
http://www.dxomark.com/Cameras/Camera-Sensor-Database/Sony/Cyber-shot-DSC-RX100-II
http://www.dxomark.com/Cameras/Camera-Sensor-Database/Panasonic/Lumix-DMC-LX7
The Sony does it very slightly more, but small enough to be ignored. From the comparison pictures it seems its less than 1/3 stop difference between an LX7 and RX100 II relatively.
So on the basis of that, especially when we add in factors such as sensor resolution I will concede that despite the aperture advantage it appears the LX7 will only narrow the gap at the tele end and RX100 II maintains an advantage due to superior sensor.
The studio results should give us a good guide to real life shooting but its difficult to tell how they perform under various lighting condition but I doubt there will be much discrepancies.
Phew!!! I hope this settles it