Canon G12 has a 10.0MP 1/1.7-inch (7.44 x 5.58 mm ) sized CCD sensor and features Digic 4 processor. On the other hand, Casio EX-10 has a 12.0MP 1/1.7-inch (7.44 x 5.58 mm ) sized CMOS sensor and features Exilim Engine HS 3 processor.
Below you can see the G12 and EX-10 sensor size comparison.
Canon G12 and Casio EX-10 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 G12 has 20% larger pixel area compared to Casio EX-10, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.