Having driven both cars and currently owning an S3, I think that the gti makes more sense on a day to day basis. It seems more fun but maybe that depends on how much you buy into the gti heritage?
Fuel costs between an gti and S3 (understand it’s not an R) have been negligible.
Illustration of what different drivers are looking for (with the caveat all GTI drivers are different and not like me).
An R owner told me "Whatever, you must get the DCC." Me: "Why?" R Owner: "It makes the suspension so much stiffer on Sport mode". Me: "I'll rarely drive it in Sport mode. I'm thinking about getting the DCC because it makes the suspension softer and more luxurious in Comfort mode."
Then, R owner told me "The R sounds so much better than the GTI". Me: "Is it more refined then and quieter in the caabin? "R owner: "No, it's louder, check out those pops and crackles and overruns."
R owner: "Great when you track it".
Me: "When I track it? WTF? I just want an affordable, relatively refined and comfortable car that isn't slow and I can have a bit of fun in."
As I say. For me, it depends entirely on your driving style and what you're looking for.