Not to suggest that I condone any form of racing on public roads (because I don't), but the OP was asking how the cars compare. According to
www.zeroto60times.com a 2013 FRS has a full 1 second advantage in both 0-60 and 1/4 mile times over a 2003 TT Quattro. It also pulls higher g's in skid pad tests. All other things being equal your twin should be the winner.
As others have already said, driver's skill can make up for what a car lacks in performance. If this is really just for fun than make it just for fun and drop the $500 bet. Get yourselves to an auto-x or HPDE. Put the money into a car payment.