Panasonic ZS7 has a
12.0MP 1/2.3-inch (6.08 x 4.56 mm ) sized CCD sensor and features Venus Engine HD II processor. On the other hand, Fujifilm X-Pro1 has a
16.0MP APS-C (23.6 x 15.6 mm ) sized CMOS X-TRANS I sensor and features EXR Pro processor.
One other difference between these two cameras that is worth mentioning is that Fujifilm X-Pro1's sensor doesn't have an 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 ZS7 and X-Pro1 sensor size comparison.
As seen above, Fujifilm X-Pro1 has a 13.3x Larger sensor area than Panasonic ZS7. 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.