Nikon D750 has a 24.0MP Full frame (35.9 x 24 mm ) sized CMOS sensor and features Expeed 4 processor. On the other hand, Nikon D300 has a 12.0MP APS-C (23.6 x 15.8 mm ) sized CMOS sensor and features Expeed processor.
Nikon D750's sensor provides 12MP more than Nikon D300'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 D750 and D300 sensor size comparison.
As seen above, Nikon D750 has a 2.3x Larger sensor area than Nikon D300. 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 D750 and Nikon D300 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, D750 has scored 93, 26 points higher than D300.