I test drove both side by side when they first came out with the S. We were looking for a toy as a second car. Drove the regular mini with a slushbox and the S without.
They were totally different cars.
The S is closer to a go-cart, but it really doesn't like bad roads, it tramlines like crazy and is noisy when you step on it. It's got ok acceleration, decent brakes and corners well - unless your roads are crap (like ours here), then it's easy to upset mid-corner. Both cars understeer if you drive enthusiastically.
The regular car is a lot slower. It's noisy at 70 to the point where you can't talk without raising your voice, and you feel like you are working hard to get it up there.
Remember the one I drove had a slushbox though, so it's not an apples to apples comparison, and these are my impressions - no flames from happy new mini owners - I personally happen to like the older minis better, but they aren't nearly as practical.
We ended up getting something totally different as the toy - a little more teutonic, but still iconic. (Wifes choice, not mine).