The Fit wins for moving stuff (cargo).
The MINI moves.
At last season's Autocross championships-
A stock base MINI old version (2005) with R compound tires
35.479 seconds 47th place on raw time out of 70, 20th overall with handicap
Vs
A modified Street Touring Fit Sport
with Dunlop Direzza Z1 Star Spec street tires (one of the best tires)
35.643 seconds 50th place on raw time out of 70, 34th overall with handicap
Both were manual transmissions, both tops in their classes.
As for potential-
For most people the MINI has more potential for performance driving. The chassis is stiffer, center of gravity a little lower, assuming you don't add a turbo or supercharger kit.
If you took the base cars and added only wider wheels and sticky tires of the same type then the MINI would have a big advantage. The stock suspension on a MINI is far better.
Overall the MINI doesn't have as many performance upgrades vs the Fit in the normal aspirated engine versions. The MINI S is a supercharged version until the current one which is turbo which began in 2007.
The older Cooper S version has many upgrades for power and can be tuned for 230-250+ HP very easily which would double the base Cooper's HP.
Don't compare the Cooper S with any base Cooper. The new turbo Cooper S has added HP but it's not as easily upgraded for power yet.