Panasonic S5 has a 24.0MP Full frame (35.6 x 23.8 mm ) sized CMOS sensor and features Venus Engine processor. On the other hand, FujiFilm AX350 has a 16.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor .
Panasonic S5's sensor provides 8MP more than FujiFilm AX350's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
Another difference between these two cameras is that Panasonic S5'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 S5 and AX350 sensor size comparison.
As seen above, Panasonic S5 has a 30.2x Larger sensor area than FujiFilm AX350. 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.