Olympus E-M10 II has a
16.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor and features TruePic VII processor. On the other hand, Olympus E-300 has a
8.0MP Four Thirds (17.3 x 13 mm ) sized CCD sensor .
Olympus E-M10 II's sensor provides 8MP more than Olympus E-300'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 E-M10 II and E-300 sensor size comparison.
Olympus E-M10 II and Olympus E-300 have the same sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Olympus E-300 has 99% larger pixel area (28.15µm2 vs 14.12µm2) compared to Olympus E-M10 II, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.