In good light, where you can stay at base ISO regardless of lens speed, the larger sensor should provide more color depth and better dynamic range - if it has comparable efficiency per amount of square mm as the smaller sensor. Canon's sensor tech seems less efficient, as it appears to do considerably worse at DR than sony-based sensors of the same size, undoing some of the size advantage compared to 1" and m43. Other apsc cameras have a more obvious advantage here.
In lower light, where you need a fast lens to maintain low iso's as long as possible, the lens speed / sensor size combo (aka equivalent aperture) becomes more important, and a 1" sensor with faster lens might beat an apsc with slower lens, even if that apsc sensor is one of sony's efficient designs.