Sony HX300 has a
20.0MP 1/2.3-inch (6.16 x 4.62 mm ) sized BSI-CMOS sensor . On the other hand, Nikon D7100 has a
24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor .
One other difference between these two cameras that is worth mentioning is that Nikon D7100'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 HX300 and D7100 sensor size comparison.
As seen above, Nikon D7100 has a 12.9x Larger sensor area than Sony HX300. 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.