Go for the Mazda, hands down. Run from the Mini if maintenance costs are a consideration.
I've had a Miata and currently drive a Mazda6. I've been incredibly happy with both. They're well built and part failures are extremely rare. With 12 years of combined ownership, I had an alternator go out on the Miata, and a problem with the nav unit on the Mazda6 (covered by warranty). My only complaint with the Mazda6 is that you store the jumper cables in the trunk, and there is no way to open the trunk with a dead battery.
My wife had a Mini when we met. It was a fun car to drive. We even managed to pack for a week long camping trip in it. It was somewhat comical, but one of our better trips.
Maintenance on a Mini is a ridiculously more expensive. Here's an abbreviated list of maintenance challenges we had over ~3 years with it. We spent more on Mini maintenance in three years than I've spent in 12 years owning Mazda's combined.
-You need $100+ specialty tools just to change the brake-pads. It's ridiculous.
-The nearly vertical windshield is very vulnerable to rock and debris strikes. We averaged a new windshield every year we owned it. I'll refrain from specific comments on my wife's driving, but regardless of circumstances, that was a lot of windshields.
-Run-flat tires are the stupidest invention ever. They are non-repairable (well, I did it myself once or twice) and are somehow magnets for anything sharp. We went through two or three from random sharp objects. Of the 4-6 tire punctures I've had in my life, only one didn't happen in that Mini. Also, never, never, ever buy the less expensive mini run-flats. The rear suspension in a mini in non-adjustable and will wear through the cheap tires in under 15K miles. Guess how I know that.
-Random coolant leaks that it takes professional technicians 3 visits to find.
-Jack points are sub-standard compared to all other brands of cars I've worked on. Every other model of car I've worked on allows you to use jack stands under the suspension to keep the suspension loaded. Try that with a Mini, and you'll do $400 in damage to the suspension. Again, guess how I know that.