Sony HX350 has a
20.0MP (1/2. ) sized BSI-CMOS sensor and features BIONZ X processor. On the other hand, Panasonic S1 has a
24.0MP Full frame (35.6 x 23.8 mm ) sized CMOS sensor and features Venus Engine processor.
One other difference between these two cameras that is worth mentioning is that Panasonic S1'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 HX350 and S1 sensor size comparison.
As seen above, Panasonic S1 has a infx Larger sensor area than Sony HX350. 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.