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, Sony A77 II has a 24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features Bionz X processor. Sony A77 II'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 D300 and A77 II sensor size comparison.
Nikon D300 and Sony A77 II 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.