Sensor size and lens aperture
As I said before, a larger sensor and a larger aperture lens will provide higher quality. It captures more light, which is what photography is all about. When you have less light to work with, the bigger senor and lens capture it more easily. Whether the difference between the G12 and HX20V is enough, that's up to the individual person to decide. I personally am aware of the difference but trade off the slighter better image quality for a more compact camera.