Nikon D3100 has a 14.0MP APS-C (23.1 x 15.4 mm ) sized CMOS sensor and features Expeed 2 processor. On the other hand, Nikon D3300 has a 24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features Expeed 4 processor.
Nikon D3300's sensor provides 10MP more than Nikon D3100'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 Nikon D3300'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 D3100 and D3300 sensor size comparison.
Nikon D3100 and Nikon D3300 have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with 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 D3100 and Nikon D3300 sensors have been tested by DxO and the results show that D3300 has a better overall score of 82, 15 points higher compared to D3100's score of 67.