Both Sony H300 and Sony RX10 III have 20.0 MP resolution sensors but Sony H300's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Sony RX10 III's sensor is 1″ (13.2 x 8.8 mm ).
Since Sony RX10 III's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Sony H300.
Below you can see the H300 and RX10 III sensor size comparison.
As seen above, Sony RX10 III has a 4.1x Larger sensor area than Sony H300. 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.