Both Nikon D610 and Nikon D7200 have 24.0 MP resolution sensors but Nikon D610's sensor is Full frame (35.9 x 24 mm ) and Nikon D7200's sensor is APS-C (23.5 x 15.6 mm ).
Since Nikon D610'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 Nikon D7200.
One other difference between these two cameras that is worth mentioning is that Nikon D7200'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 D610 and D7200 sensor size comparison.
As seen above, Nikon D610 has a 2.4x Larger sensor area than Nikon D7200. 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.
DxOMark Sensor Scores
Both Nikon D610 and Nikon D7200 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, D610 has scored 94, 7 points higher than D7200.