I am not talking about iso performance here. I am talking about lens aperture at 28 fov. The rx100 @28fov is f1.8 vs the Ricoh @f2.8.
And the GR APS sensor still substantially outperforms the 1" sensor in stops.
The GR in low-light is 3 stops faster than the RX100, both wide open, both at 28mm.
A stop is a stop.
So if the RX100 wide open f/1.8 at 28mm needs 1/60 second, the GR at f/2.8 will be at 1/250 sec.
In order for the RX100 to get that same 1/250 sec. it will need to crank the ISO 2 stops, but it will be about 5.5x noisier in the shadows. Lots of pink speckles. It gets much worse for the RX100 above ISO 800.
Also the GR DOF is shallower than the RX100 at measured aperture. At 28mm the RX100's DOF on a 10 ft. subject shot at f/1.8 is 1.52 ft. The GR at f/2.8 is 1.31 ft. The laws of physics say it cannot get any better on the RX100. The GR f/2.8 will always have a shallower DOF and brighter image than the RX100.
All this will apply on the GR at the crop 35mm as well, and at the 21mm with adapter.
The RX100 is smaller, cheaper, and has a zoom. But at no FL can its f/1.8 lens make up for that 3x larger sensor in the GR. It's within 20% at ISO 100 at f/1.8, but that's as close as it gets. From there on the GR pulls away. The RX100 zoomed out or stopped down more and more resembles a P&S while the GR never loses its APS-C (DSLR or Fuji X) equivalency. That's the design choice of a large sensor, fixed lens.
And the Sony RX1 full frame has a similar advantage over the GR. It's a full stop on the lens alone plus about 1.3 stops on the sensor, pulling away above ISO 1600 substantially. Of course you have to add $2,000 to get there over the GR whereas the gap between the GR and RX100 is $150 MSRP.
They each have their own niche. I've used the RX100 and really like it. If I had to get a travel size P&S it would be my choice, especially for outdoor available light shooting.