We had a MINI One with 15s for a number of years, plus I've had a play in a few other MINIs with the 15" OEM and I find them too skittish, not enough grip on the tyres provided (cornering and wheels spin wise), and the larger sidewall I think for me just tips them into the "too squishy" zone. But not a lot in it, I'd rather have decent 15" wheels than 17" wheels if I was looking for the best overall package. Trouble with 15" wheels for a lot of people seems to be the tyre options and certainly aftermarket brake options are very limited. But they are brilliant fun.
If you don't want to take my word for it, we asked Mike Cooper a long while back why the challenge Coopers where decked with 15" wheels, he just replied something like "they provide the most fun on the track".