Canon G1 X II has a 13.0MP 1.5" (18.7 x 14 mm ) sized CMOS sensor and features Digic 6 processor. On the other hand, Canon G1 X has a 14.0MP 1.5" (18.7 x 14 mm ) sized CMOS sensor and features Digic 5 processor.
Below you can see the G1 X MII and G1 X sensor size comparison.
Canon G1 X II and Canon G1 X have 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 Canon G1 X II has 9% larger pixel area compared to Canon G1 X, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.