Panasonic G9 has a 20.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor . On the other hand, Panasonic GX1 has a 16.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor and features Venus Engine FHD processor.
Another difference between these two cameras is that Panasonic G9's sensor lacks 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 moire occurring in certain scenes.
Below you can see the G9 and GX1 sensor size comparison.
Panasonic G9 and Panasonic GX1 have the same 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 Panasonic GX1 has 27% larger pixel area (14.21µm2 vs 11.16µm2) compared to Panasonic G9, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.