-performance (turning, power, etc.)
in straight line, mini cooper S hands down. More torque, more power, Mini will outrun the miata in the straight
Cornering, miata hands down. Light weight, rear wheel drive, double wishbone front and multi-link rear suspension. This combination screams for more corners. Look on SCCA autoX results to give you an idea how fast the MX-5 is compare to Mini Cooper S. (C stock car vs G stock car)
-upkeep (insurance, mpg, etc.)
convertibles may be more expensive to insure depending on where you live. The possibility of someone slashing your top may raise the insurance rate.
fuel consumptions should be pretty close in real life situation and largely depends on driving habit (numbers posted are not a good representation of realistic consumption). They are both relatively light and have fairly efficient engine.
-reliability (any breakdowns after ... miles?, expensive parts?)
Both cars are relatively new. Miata/MX-5 are known to be reliable machine that last for a long time before something needs to be repair. They are simple and easy to work on.
I do not have much personal experience with the mini cooper S, but the earlier ones do have some reliability issues that should be fixed by the 2009 models
-comfort and feel
The miata is a very comfy car for a convertible unless you are really tall (6ft plus) I'm 5' 10" and therez still plenty of room behind the seat. it is hard to compare comfort between the two because one's too firm may be someone else's too soft. Go test drive them both to get a good answer out of this question.
and finally, FEEL! I dare say Mini is no where near the MX-5 in terms of feel. You know exactly what the car is doing in an MX-5, you tell it exactly what you want to do and it does it! the car communicate very well with the driver. Go take one out for an extensive test drive. The feel is nearly impossible to be describe by words. Best to feel it ;)