Both Nikon D7100 and Nikon D610 have 24.0 MP resolution sensors but Nikon D7100's sensor is APS-C (23.5 x 15.6 mm ) and Nikon D610's sensor is Full frame (35.9 x 24 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 D7100.
Another difference between these two cameras is that Nikon D7100's sensor lacks 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 D7100 and D610 sensor size comparison.
As seen above, Nikon D610 has a 2.4x Larger sensor area than Nikon D7100. 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
DxOMark is a benchmark that scientifically assesses image quality of camera sensors. It 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. Nikon D7100 and Nikon D610 sensors have been tested by DxO and the results show that D610 has a better overall score of 94, 11 points higher compared to D7100's score of 83.