No question - S3.
The A3 Sportback 2.0T (147kw) FWD DSG was easily able to take my old 325i AT (160kw) in a straight line at Jozi altitude. The 325i got off the line faster (it had M-Sport pack with 255 R17's at the back) while the A3 burnt its front tyres, but the A3 caught up and overtook quite quickly. The 125i is only a little lighter then the 325i and has thinner tyres, so I don't see it having much of an advantage.
Now you're talking about the S3 which has AWD traction off the line and 195kw less ~5% altitude loss rather than 147kw less 17% altitude loss, and it's in a different league. The biggest issue with the A3 was the shocking understeer which the S3 *should* quell.
As for RWD fun, I honestly couldn't unsettle my 325i M-Sport in the dry. It didn't have anywhere near enough power to overcome the grip of the 255's at the rear. The 135i is a different story; you can really play with it in a way that is quite difficult with the quattros.
Despite all the raving about the DSG gearbox, it may be great once on the move but I have my doubts about the electronic clutch actuation combined with turbo lag on take-off. You get a double-lag effect. The multitonic A4 3.0 Cabrio I owned really showed the intermittent failures of the electronic clutch actuation system and after three years of fighting with Audi I eventually sold the car and made it a somebody else's problem. Thankfully Audi changed the clutch system in the >= 2004 multitronic boxes and the DSG boxes. Also, gone are the days of over-engineering the gearboxes. E.g. on my A4, the engine torque was 310Nm and the gearbox tolerance only about 330Nm. If you have plans of chipping the S3, the engine may cope with the extra torque, but the DSG box may not; be sure to do your research. Honestly, if I was going to chip my S3, I'd buy the manual; if I bought the DSG, I'd keep it stock.
I've never driven an S3 (or in fact any Haldex-based AWD vehicle). Before the last two Beemers I had an Audi RS2 Avant which had the more traditional Torsen-based AWD system (with 50/50 split, 232kw / 410Nm) [which was fantastic to drive]. I have also driven the old B6 S4 4.2 [good drive] and A6 3.2 quattro [may as well have been FWD].