Have you tried processing the Jpg file similar to what you did with the RAW file?
The RX100 jpegs actually have a LOT of processing latitude, way more than a lot of jpegs do. The Fuji X-100 and X-Pro jpegs also have loads of latitude. But with the RX100, there are still limits to what you can do with WB, and at higher ISO there are some pretty ugly NR artifacts that even show up and reasonable viewing sizes. With the raw files, you get more latitude (even though you might not need it often) and you get reasonably "pure" noise. There's plenty of noise at 3200 and 6400 but there's also a LOT of detail and it can clean up reasonably well in Lightroom. There's a lot less space between raw and jpegs with these files than with a lot of cameras, but there's still a difference.
Just for example, here's a shot my wife took of me, directly into the sun - I realized the mistake right away and she took another from a better angle, but I decided to play with this anyway.
In the OOC jpeg, my face is virtually black as you might expect:
View attachment 59039
Using as crude a tool as snapseed on my ipad, this is what I got when I processed the jpeg and raised my face out of the darkness. Remarkably clean, but its processed for the clouds, so my face has a bit more texture than it otherwise might. I've since played with it in Lightroom on my mac and its remarkably clean with ZERO NR applied beyond the lowest NR setting in-camera. I find this pretty amazing. I remember fighting with Olympus
raw files from everything prior to the OMD and not being able to pull shadows without horrendous noise. This is with a jpeg and there's essentially NONE. This is a recent development in my experience:
-Ray