JD Power and assoc long term brand reliability ratings place Audi (and VW) way WAY down at the bottom, while BMW is close to the top. I know a lot of people who are pleased with their leased Audi, but everyone I know that bought their audi is disgusted.
However, the kicker is the repair costs. By all accounts, the Audi is absurdly expensive to repair. A friend recently had her clutch done in her 98 A4 for approx $900. By comparison, the BMW is relatively cheap (so long as you don't take it to a dealer).
Of course, this isn't head to head, but as a rule of thumb I would not get an Audi (or VW, or Saab....)