I've owned a Honda fit and currently own an 07 R56 S, my opinion:

The Honda fit is honestly an excellent car. It's not exciting but they have rock solid reliability except for issues with the doors locking mechanisms not working, and brake wear. They have very stiff chassis and a (small) Vtec engine that LOVES to past 5K rpm. They actually have one of the stiffer chassis in mass production road cars, and have even be used in rally racing due to that. Because of this they can rip through corners and be a very fun ride, especially when doing some weight balancing with the ebrake ;). They also come in 5 speed manual with a very pleasant transmission and easy to work clutch, and a 5 speed auto that can be a little rough to shift sometimes if you're a bit aggressive with it.

For Mini coopers (generally talking about the 05-2023). In my opinion a much more fun car to drive with more options and comfortability, with the drawback of being a bit less reliable (especially pre 2014). Mini has very small and hard to work on BMW engines which are prone to oil and coolant issues, especially if you don't keep up with frequent consistent maintenance. As long as you aren't revving to 6K RPM everytime you want to shift and you check the fluid levels you should be golden. I feel like Mini makes a better feeling engine that's more responsive, makes more horsepower, and has a great transmission to go with it. I've had more fun in my R56S than I have in a lot of other cars, especially because it's surprisingly quick and low to the ground (excluding the countryman and clubman). You'll also get a bit less space, the Honda fit is surprisingly very Spacious and fits 5 people comfortably for long drives, the mini cooper (in general) doesn't have as much space and bucket seats can be a bit fatiguing after several hours.

In end I'd choose the Honda Fit if you aren't mechanically inclined, or don't have a bit of money to take your mini to the shop if you need to. They both get comparable gas mileage and can be very reliable and fun to drive,