The only thing I have the driving experience to compare them with are the Pirelli Euforias, so it's as much a comparison on the difference between very stiff-wall run-flats and non-run-flats as it is a comparison between two specific tires makes.

As far as what you give up - the ASXs are perfectly good for street driving. I still have the standard Mini traction problem on hard launch in 1st and even 2nd and around corners. Without adding/altering suspension components (my first choice would be swapping out the shocks), I'm not convinced that you'd really notice a serious difference between these tires and much more expensive ones, not in spirited street level driving.

If I get around to autocrossing the Mini this year (which I may - after 15+ years of autox, I backed out of the sport a few years back, but my Mini makes me want to go rocketing around the cones again), I may make several changes in the suspension, at which point I'd buy autocross specific tires and wheels anyway. On the other hand, a well-set up autocross car is not a comfortable car to drive on the street, so... perhaps not.

That's not much help, is it? But without doing back-to-back testing, I can't give a more useful answer.

 

I like the General Exclaim UHP 215/40/ZR17. I bought them off the tire rack and was a bit skeptical about them. Once installed I have not looked back. They handle great on wet and dry pavement and are pretty quiet. Now you have my 2 cents worth...

 

How long have you had these?
I saw them on Tire Rack and am interested, but have not had luck with General tires in the past.

 

I am also going with the General Exclaim UHP very soon. I have Pirelli P Zero Nero's as my last set, and they were wonderful... but you can't beat the price on these generals, nor the ratings. I read through about 300 reviews and was very impressed by what everyone had to say. I'll be sure to post my findings soon.