Nikon D300 has a 12.0MP APS-C (23.6 x 15.8 mm ) sized CMOS sensor and features Expeed processor. On the other hand, Olympus E-M1 II has a 20.0MP Four Thirds (17.4 x 13 mm ) sized CMOS sensor and features TruePic VIII processor.
Olympus E-M1 II's sensor provides 8MP 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 D300 and E-M1 II sensor size comparison.
As seen above, Nikon D300 has a 1.6x Larger sensor area than Olympus E-M1 II. 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 D300 and Olympus E-M1 II sensors have been tested by DxO and the results show that E-M1 II has a better overall score of 80, 13 points higher compared to D300's score of 67.