Sony A37 has a
16.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor . On the other hand, Ricoh GR III has a
24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor .
Ricoh GR III's sensor provides 8MP more than Sony A37'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.
One other difference between these two cameras that is worth mentioning is that Ricoh GR III'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 A37 and GR III sensor size comparison.
Sensor Size and Resolution Comparison image of Sony A37 and Ricoh GR III Cameras
Sony A37 and Ricoh GR III have the same sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Sony A37 has 49% larger pixel area compared to Ricoh GR III, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.
Sensor size sets the circle of confusion, so it drives how much depth of field each
of these bodies gives you at a given aperture. You can calculate it exactly for the
Sony A37
or the
Ricoh GR III ,
including hyperfocal distance.