I know most on here are going to prefer the S3, as most probably currently own one, and the same goes for asking on a BMW forum, most will prefer their BMW's.
However, from looking on various sites, reading/watching reviews etc I think it's clear (even from my own limited experience now) that the BMW is the better drivers car and the S3 is the better looking, both inside and out (I do think the Sat Nav/Screen in the BMW looks better though, the screen in the S3 looked almost pixelated which was a bit of a surprise for a virtually brand new car).
One main thing for me is going to come down to price, I was initially looking at a used M135i but any that were anywhere near the spec I would like (5 door, auto, HK, Pro Media at least) are about £24k for one that's a couple of years old. With the discounts available I could get a brand new M140i with these options and a few more for a bit over £27k (Depending what options I go for) but this really would be my limit as I was never going to spend this much until I found out by throwing another couple of £k at it I could get a brand new one, to my preferred spec....... the 2016 S3 (6k miles on the clock) I tested yesterday was at a bargain price of £32,987!
and the sales girl told me it's quite a good price as they have just recently reduced it by £1k (that was not sales bull either as I had seen the car at that price a few weeks back)!
If I was to get an S3 it would have to be a used one, probably a couple of years old so it would be around the £25k-£26k bracket, so again, for the extra, I would end up getting my first ever brand new car (BMW)
Decisions decisions!