Panasonic G9 has a 20.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor . On the other hand, Fujifilm X-E1 has a 16.0MP APS-C (23.6 x 15.6 mm ) sized CMOS X-TRANS I sensor and features EXR Pro 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 moiré occurring in certain scenes.
Below you can see the G9 and X-E1 sensor size comparison.
As seen above, Fujifilm X-E1 has a 1.6x Larger sensor area than Panasonic G9. 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.