Sony RX1 has a
24.0MP Full frame (35.8 x 23.8 mm ) sized CMOS sensor . On the other hand, Sony RX1R III has a
61.0MP Full frame (35.8 x 23.8 mm ) sized BSI-CMOS sensor and features Bionz XR processor.
Sony RX1R III's sensor provides 37MP more than Sony RX1's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
One other difference between these two cameras that is worth mentioning is that Sony RX1R III's sensor doesn't have an anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moiré occurring in certain scenes.
Below you can see the RX1 and RX1R III sensor size comparison.
Sensor Size and Resolution Comparison image of Sony RX1 and Sony RX1R III Cameras
Sony RX1 and Sony RX1R III have the same sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Sony RX1 has 150% larger pixel area compared to Sony RX1R III, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.
Sensor size sets the circle of confusion, so it drives how much depth of field each
of these bodies gives you at a given aperture. You can calculate it exactly for the
Sony RX1
or the
Sony RX1R III ,
including hyperfocal distance.