Fujifilm S1 Pro has a
3.0MP APS-C (23 x 15.5 mm ) sized CCD sensor . On the other hand, Sony A37 has a
16.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor .
Sony A37's sensor provides 13MP more than Fujifilm S1 Pro'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.
Below you can see the S1 Pro and A37 sensor size comparison.
Fujifilm S1 Pro and Sony A37 have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.