Sony RX100 III has a 20.0MP 1" (13.2 x 8.8 mm ) sized BSI-CMOS sensor and features Bionz X processor. On the other hand, Sony RX1 has a 24.0MP Full frame (35.8 x 23.8 mm ) sized CMOS sensor .
Below you can see the RX100 III and RX1 sensor size comparison.
As seen above, Sony RX1 has a 7.3x Larger sensor area than Sony RX100 III. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.