Fortuitous you started this thread today, as I have been considering this myself over the last few weeks. I'm going to turn this into a discussion so bear with me.
I love my S3. I love the size, I love the fuel economy, and I like how it drives. I like the big aftermarket, I like the way it looks, I like the build quality of the interior. I like how it's near invisible (especially in silver) and how it can hold its own against newer cars (because it isn't stock).
I like how the motor (sans rods) is quite rugged, robust, and can handle lots of power. I like how the transmission can also hold 2x the power easily. I like how the Haldex system can also handle anything you throw at it.
However...
The AWD system, compared to a proper one, is ****. Whoever here has been in an Evo or an STi can attest to that. I don't like its unpredictable nature sometimes as a result of this. I don't like the incessant understeer upon entry, either. Now I realize you can make ANY platform handle with enough money thrown at it, but that's besides the point. Spending thousands on suspension mods to improve it (and still not matching a stock Evo), disappoints me.
While it does make good power for a 1.8T, it is still a gutless **** below 2500rpm. I know for people who are used to turbo engines that that is a good powerband, but for someone like me who has owned responsive NA motors of varying size, it is disappointing. My old CRX SiRII had a better powerband (relatively). Much lower torque, but much better response and MUCH less weight (880kg with half a tank and a sub in the back
) meant I never, ever had an issue with it being so gutless. Also, the fact that it runs out of steam so early sucks. Fun is nearly over by 6500rpm on my hybrid setup. A Honda K20 engine, something everyone beats on for being torqueless, feels much better than the 1.8T before boost. A well sorted K20/K24 hybrid makes the same power a typical hybrid turbo setup makes, too. Couple that with the 200kg advantage the EP3 has and it really doesn't feel lacking. Not epic, but not lacking. My best friend has one and my car runs neck and neck with his.
The fact that you need to upgrade EVERYTHING to make over 300 to the wheels also sucks. Stock injectors won't do it. Stock turbo won't do it. Stock rods won't do it. Stock downpipe won't allow it. And the list goes on... That's not even getting to the Hitler of ECUs that is on the car.
Couple that with the fact that it is the single most cramped and tight engine bay I've ever seen, along with the most needlessly convoluted and complicated layout of everything... Then add the mediocre brakes.
Think about it this way. The parts you need to make the car handle and go properly:
Suspension wise, you need camber adjustment front and back (especially if lowered). You need thicker ARB as the car is set up too soft. I'm assuming any car owned by an enthusiast will have shocks and springs so I won't use it as a disadvantage.
To "fix" the AWD, you need a haldex controller. To improve it even further, you need LSDs (stock on a non-base Evo).
To improve power past 300 horsepower, you need injectors. And downpipe. And turbo manifold. And a hybrid/BT. And a TIP. And an intercooler solution. and and and....
Why spend all of thousands of dollars on parts, and thousands more on labor, to not even match the all around characteristics of a mapped Evo?
The only reason I bought my S3 is because it was well modded and I couldn't find an economical and powerful all-rounder that was better for what I paid for it. If I had an extra $8000 to buy an Evo 8, I would have.
Don't get me wrong, I'm not against improving it. I just don't want to cross a certain $/hp ratio. It's in the shop now getting rods, meth, lwfw, exhaust, and TIP. I'm saying I wouldn't have done those things if
@Chlippo hadn't done so many supporting mods before I bought the car. I also invested in a Liquid gauge and Phoenix Gold components and amplifier.
In summary, I think if you bought your S3 to make it fast and run with "quick" cars, you bought the wrong car. If you want a quick, well built hatchback that will work in water or snow, then I think you bought the best car. Decide what you want with it, and decide if you really want to invest ALOT of money (double that amount if you don't do the labor yourself) to make it run with the best of them, then do that. My uncle told me something once that didn't make much sense then but does as I got older.. You can buy a donkey. You can train said donkey. You can work long and hard on that donkey. But it's always better to buy a racehorse.
Lastly, case in point... Chlippo sold his car to me and bought an Evo.
And the quickest car in my fleet, currently, is a diesel powered automatic A6 Estate! lol, which happens to go over speedbumps quite comfortably. 
