Both Olympus SZ-30MR and Fujifilm X-Pro1 have 16.0 MP resolution sensors but Olympus SZ-30MR's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Fujifilm X-Pro1's sensor is APS-C (23.6 x 15.6 mm ).
Since Fujifilm X-Pro1's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Olympus SZ-30MR.
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 moire occurring in certain scenes.
Below you can see the SZ-30MR and X-Pro1 sensor size comparison.
As seen above, Fujifilm X-Pro1 has a 13.1x Larger sensor area than Olympus SZ-30MR. 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.