I haven't driven an Exige S, but I did take a test drive in a slightly-modified (intake and exhaust) Elise once. A hell of a car, and really no comparison for the GTI, obviously. Seemingly endless amounts of grip, and while I didn't push it anywhere near hard enough to experience a loss of grip, it felt like the stereotypical mid-engine RWD car around corners.
For a car with no power-assisted steering, it was amazingly light at a stop, and at speed, it was almost too light for my tastes. It definitely had copious amounts of feedback though. And the sound, holy shit the sound. The sound alone from revving that engine to 8,000 RPMs as it sits right behind you is something you'll never forget (unless you DD a Ferrari maybe).
It's a great race/track car, but on public roads, I think I'd rather have a S2000 or the like, even at the expense of maximum grip and speed levels. The Elise/Exige would definitely be faster, but the S2000 is more fun to drive (IMO). Just my two cents...