For snow, I would take the Audi with awd any day over the M3 with rwd. No way does rwd with snows equal awd unless you run summer tires on the awd or bad all seasons.
But an M3 with snows does OK. I drive mine year round in NH and have been driving my E36M3 in NH on snows for 8 years and other rwd cars on snows up here for 20 years.
I agree that awd with non winter tires is not great. My wife's 535xi on PS2s was next to useless but I expected that and bought a set of snow wheels.
Audis are great in snow and rain, but as noted, there may be a price to pay in the dry. Still, some of the new ones are pretty competitive. One car magazine had the Audi with 4.2l V8 and 450 hp, I think it was the S5, soundly beating the M3 on the track. Other magazines have the M3 ahead. It is close. I would not be unhappy with either car.