Cant really comment on a Stage 2 S3, but I had a Stage 1 APR S3 (circa 310bhp) and now own a B8 S4. I’ve only had it for 3 months so others will be able to give you more info than I.
I'd say that it would be quite even between a Stage 1 S3 and Stock S4, certainly not a great deal in it. I suspect a Stage 2 S3 would comfortably have the legs on a Stock S4.
S4’s tend to make over their quoted figured, circa 340-350 bhh stock.
Those are serious numbers you have in your car (have you uprated the turbo too?), which no doubt cost a fair few quid to get there. Assume it’ll take similar money to get an S4 to where you want it to be.
HOWEVER all that being said, tuned vs stock is hardly fair. If you were to spend 1.5K ish at a place such as MRC (Where I intend to go once my warranty runs out) You could have a Stage 2 set up giving you in the region of 480bhp and 580nm, which makes it a whole different kind of animal.
They are 3 litre SUPERCHARGED engines so the power delivery is very different to what you currently have, much more linear. There is no lag whatsoever.
Handling is good for what it is. I have the Audi Drive Select with Sports Diff and in Dynamic mode I think it handles very well indeed. It isn’t as nimble as the S3, given the significant weight difference but it has very high grip levels.
Bad with OVERSTEER?? No, in Dymanic mode you can get the car to oversteer if provoked.
If you mean bad for UNDERSTEER – dependant on how you drive / what setting you are in (assuming you get a car with drive select) it is prone to understeer in comfort mode, BUT in normal driving conditions I would say that it is better than my old S3 (stock suspension) which had far worse understeer characteristics. Yours will no doubt be different with the uprated ARB and suspension changes.
Common faults in early cars were the Water Pumps (which were replaced under a recall – check to be sure) and the Thermostats are prone to failure. Other than that that car seems to be quite robust.
From a personal point of view, I needed a car that was more practical as I now have a wee boy. I loved my S3 and was actually looking at getting another in sportback form. I couldn’t stretch my budget to the 8V, so it would have been another 8P. I’m glad however that I went down the S4 path, as it suits my need perfectly just now. Performance is good out of the box and with some money spent it can become so much more. Its plenty big enough in the rear for the wee man and his car seat / ancillaries which is ultimately what I needed it for. Wouldn’t change it.