Today the Sony Rx 100 III matches specwise nearly 100 % exact the Sony DSC - R1:
The RX 100 III has the much much smaler Sensor (8.8 x 13.2 mm instead of 14.4 x 21.5 mm) but also the much much more wide open lens: 1.8 at the short focal length instead of the 2.8 of the DSC - R1. So it is a complete draw at the short focal length range: Both cameras will offer the same depth of field when it comes to a focal length that equals 24 mm to perhaps 50 fullframe.
At the long focal length range the RX 100 III ends at 25.7 mm that means, it´s one inch sensor equals 70.09 mm fullframe. The DSC - R1 ends at 71.5 mm that equals 120 mm fullframe (so the crop factor is about 1.678). But again the pictures will look perhaps a bit more similar as you might expect: You have to crop the 20 Megapixel pic of the RX 100 III by factor 1,712 wich means it will you show you 3192 x 2128 pixel, a bit more than 6.4 Megapixel, wich is absolutely o.k. But with its 2.8 aperture there is no big disadvantage, depth-of-field-wise-spoken, in comparison with my 1 kg weighing gigantic R-1 superbaby. More than half of the advantage of the longer focal length of the R1 is destroyed by the not-so wide-open largest apperture of 1:4.8 at the long end! The advantage of the "old chap" is about factor 1.639 wich means barely 1.33333 f-stops better separation instead of 3 f-stops better separation that the R1 would have had with a 2.8 maximum apperture at maximum focal length (which would have resulted in a 2 kg Camera in a price range of perhaps EUR 4.000,--......)
As a modern, affordable, extrem priceworthy successor of my "superbaby", now in the EUR 500,-- range, with its one inch sensor, the RX 100 III is owned by two close friends of mine. It is the perfect backup camera for the larger Professional Cameras from Nikon or Sony for example. The Rx 100 III shows incredible colors; colors that looks perfectly in place, Really "Leica-like" if you switch the saturation to minus 1.
That said: Although the modern Sony RX 100 III is 3 times lighter and 3 times smaler than my "large Bomber", it has pretty much the same image qualities and a similar color rendering.
For reaching absolutely perfection in color rendering, i switch to adobe RGB and the resulting jpeg files are treated as if they were sRGB!
The main adventage of the 10 years younger RX 100 III is: it can shoot even nice HD-videos. The DSC - R1 can´t take videos.
Sometimes I am now joking and telling Stefan or Peter, that my DSC - R1 is shooting great pictures (simply by it´s optical qualities), whereas the RX 100 III is just calculating great pictures. So you can say, the RX 100 III is just a kind of a braggart. A dirt patch with some silikon in it ;-)
Here is a nice pic of my daughter, which shows the incredible sharpness and the perfect colors of the Sony DSC - R1.
I L O V E it!
Shot with the 13 year old Sony DSC - R1 in adobe RGB and treated as if it were sRGB. Straight out of camera. The size was reduced by just using the jpeg and opening it in the Olympus viewer 3 software. Sharpening of the size reduced image was set on + 5.