Nikon D5200 has a 24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features Expeed 3 processor. On the other hand, Sony A37 has a 16.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor .
Nikon D5200'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.
Below you can see the D5200 and A37 sensor size comparison.
Nikon D5200 and Sony A37 have 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 (22.87µm2 vs 15.28µm2) compared to Nikon D5200, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.
DxOMark Sensor Scores
Both Nikon D5200 and Sony A37 sensors have been tested by DxoMark. DxoMark scores camera sensors for color depth (DXO Portrait), dynamic range (DXO Landscape) and low-light sensitivity (DXO Sports), and also gives them an overall score. Of the two cameras that we are comparing, D5200 has scored 84, 9 points higher than A37.