Sigma DP2 Quattro has a
20.0MP APS-C (23.5 x 15.7 mm ) sized CMOS (Foveon X3) sensor and features TRUE III engine processor. On the other hand, Sony RX1R has a
24.0MP Full frame (35.8 x 23.9 mm ) sized CMOS sensor .
One other difference between these two cameras that is worth mentioning is that Sony RX1R'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 DP2 Quattro and RX1R sensor size comparison.
As seen above, Sony RX1R has a 2.3x Larger sensor area than Sigma DP2 Quattro. 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.