The larger sensor simply allows for higher quality photos. I assume the very low noise ratio will give a photo from a fullframe just a little more of a "professional" look.
The people using fullframes invest in their equipment because they spend a significant amount of time making photos. Any professional will probably carry a fullframe. So naturally the collection of fullframe photos out there is of much higher quality.
But is this statement still popular? Sensors have improved dramatically the past years. Large sensors where obviously better in the past, but now the small sensors are getting better. Software corrections fix most of the problems these days. Micro four thirds are getting popular because most people don't even see the difference anymore.
