I agree with 92dxman, the OP wants a Mazda 3. Very similar power to the SVT in a better handling package that is also competitivley classed for autocross.
Full disclosure: I currently have an SVT Focus as a semi-daily driver and track car.
If you're stuck on the original two, I'll offer my (perhaps biased) opinion on both. As others have noted, the MINI is a better autocross car, but the Focus is hands down a better street car. In fairness, I've only driven the MINI S and the convertible base model, but both were choppy and, in my opinion, uncomfortable. The ride in the SVT is, again in my opinion, the perfect combination of ride comfort with sporty handling.
The fuel economy difference is not as bad as people here are suggesting. I don't know what the MINI is rated, but the 25 mpg or whatever the Focus is rated under the new EPA system is crap. I routinely get 30+mpg on the highway and 27 or so in mixed driving.
I also don't know what all this rolling stuff is about, but I routinely track my stock SVT on NT01s and never lift more than one wheel, and rarely that. I don't know how Per won his beer, but my guess is that it was a regular Focus (not SVT) on Hoosiers or something similar on a fairly grippy surface going through a pretty extreme left-right-left.
While it is true that an LSD wouldn't hurt the SVT Focus, it wouldn't be my first upgrade. I think what it needs more than anything is camber plates up front and the adjustable rear subframe from Ford Racing in the rear. After that, I'd stiffen the springs and upgrade the shocks accordingly. By then it should really be needing that LSD, but, at least for the tracks I run, more lateral grip is what I could use most.
That said, my local track mostly has high speed sweepers where I'm at or near the top speed of most autocross courses (and in 3rd gear). If I was having to slow way down and really get on the power hard coming off a corner in 2nd I might sing a different tune about the LSD.