I only owned a the quattro version, so wouldn't be able to say much about the difference between that and the FWD 2.0T.
In comparison to other FWD cars I've owned, I found that it's like a really comfortable seat or something else high quality that slips into the background but you wouldn't want to be without. You notice the wheelspin and generally lower sense of security in poor conditions when driving a 2WD car after 4WD. It doesn't improve the braking or grip when you're not accelerating, but you can feel the 4WD kicking-in when making standing starts or during spirited driving (especially on slow corners). It goes without saying that it was also massively useful driving on solidly frozen icy roads in the winters of 2009 and 2010.
On the older A3s (with Haldex Gen 2 I think), I could actually feel the power shuffling from front to rear. In my new S3 (with Haldex Gen 3/4), it's much quicker to react and you can't really feel it shuffling the power. I understand that 2.5% of power is always sent to the rear wheels, so it's a true 4WD system - but not locked into 50:50 at all times.
You lose a bit of boot space (370 litres reduces to 310 or so) and there is probably a fuel penalty from the weight - but I'd find it very hard to go back to 2WD.