Olympus E-300 has a
8.0MP Four Thirds (17.3 x 13 mm ) sized CCD sensor . On the other hand, Olympus E-M5 III has a
20.0MP Four Thirds (17.4 x 13 mm ) sized MOS sensor and features TruePic VIII processor.
Olympus E-M5 III's sensor provides 12MP 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-300 and E-M5 Mark III sensor size comparison.
Olympus E-300 and Olympus E-M5 III have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.