Warranty or different car is sound advice tbh. But you need to consider how much it will cost to buy a different car that will either match or better a tuned S3 on performance. There arent many unless you get one with a few miles on the clock so you wouldnt have a warranty anyway. You also need to consider the additional running costs of said car since the S3, provided it doesnt go wrong and you dont hammer it all the time, is a pretty cheap car to run.
I was looking at getting an older RS5 before I bought the S3. But what put me off was the £500 a year road tax v £190, and 26mpgs versus 40mpgs I get daily driving, let alone the extra wallet raping on tyres and servicing / repairs. Since going stage 2 my S3 is probably almost as quick as the older Rs5 now anyway. The RS5 is a thing of beauty, and pretty rare car, not to mention that exhaust note but I don't regret my decision.
If you choose the modify route then you have to accept that its probably going to break something expensive sooner or later and you will just have to take the hit. As said above there is a lot to go wrong on these cars and it could easily end up being a money pit (mine has a bit, although not the fault of modifications). On the plus side many components are shared with other VAG based cars and there are loads of them around so things like second hand diffs, engines, etc are freely available and not too much money. Modding the car will have some impact on resale appeal / value if you decide to move it on.
If you don't get all your servicing done at Audi this can be problematic with warranty claims too, as I and others have found out. Keeping full audi history to have a better chance of your warranty paying out is a necessity and an ongoing expense. With no warranty you van use an indie garage at half the cost.
So it's not an easy one to call it depends how desperate you are for it to be faster, how much cash you have, and whether you're a risk taker. If you are happy to take a risk and like the car a lot then forget the warranty and tune it, although personally I would forget stage 1 and replace the intake (as a minimum) and go for a custom tune (stage 2). Don't forget to factor in the hike in your insurance with mods declared. Mine doubled.
If you dont want the risk then extend the warranty and keep it standard, or if you've got cash to burn buy a different faster car.
