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, Nikon D850 has a 46.0MP Full frame (35.9 x 23.9 mm ) sized BSI-CMOS sensor and features Expeed 5 processor. Nikon D850's sensor provides 34MP 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.
Another difference between these two cameras is that Nikon D850's sensor lacks 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 D300 and D850 sensor size comparison.
As seen above, Nikon D850 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.