I don't have a bose system in my a3 but I'd assume it would sound better. With the wiring adapters you would still keep the standard sub/amp running and the speakers (rear) running through the amp so there won't be any loss of sound/power. Most decent head units give you more options to adjust the sound, ie more than just the normal equlisers would (jazz, rock, pop etc).
Most new headunits will also be 4 x 50 watts minimum nowadays too. Whats the output on the standard stereo?? If power rating is the same then there probably would be much difference but again, you will still have more flexibility of how you want it to sound in your car.