Canon G7 X MII has a 20.0MP 1" (13.2 x 8.8 mm ) sized BSI-CMOS sensor and features DIGIC 7 processor. On the other hand, Canon G1 X III has a 24.0MP APS-C (22.3 x 14.9 mm ) sized CMOS sensor and features DIGIC 7 processor.
Below you can see the G7 X MII and G1 X III sensor size comparison.
As seen above, Canon G1 X III has a 2.9x Larger sensor area than Canon G7 X MII. 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.