the gtr is nice and sexy and will be a head turner, but remember maintenance will be more than the s3, also the s3 will be cheaper to insure in most places. s3 is more comfy, nicer ride, better handling, better fuel consumption. performance wise it ist that much slower than a gtr, 0.5 seconds to 100 isnt noticeable.
also the s3 is vastly different to a golf, in every aspect, engine, gearbox etc. has heaps of tuning potential but will cost roughly as much to tune as a GTR.
in the end it comes down to personal preference. the s3 can be had in 3 or 5 door. so if you have a family, its much more easier to go audi.
also consider police attention, GTR is pretty bad, while the s3 is seen more as normal car.
but if your going loosely on looks, GTR will win hands down