My 2007 MCS has 16 inch wheels with 196/55/16 tires onboard. I recently completed a trip to New England with the following results.

My odometer's final reading for the trip was 487.7 miles. My GPS's final reading was 492.8 miles. This is about a 1% deviation in my favor for warranty purposes.

My speedometer read was from 2.5 to 3.0 MPH faster, than my Garmin GPS, depending on how fast I had the cruise set.

 

In general larger diameter tires than OEM will make your speedometer/odometer read lower, while smaller ones will make them read higher.

I'm running the exact same size wheels/tires (for now) on my '07 MCS as you. My Garmin shows the speedo to read about 2-5mph faster than reality as well. The margin of error gets higher as my speed increases, at normal cruising speeds it's like 3mph exactly. Never checked the odometer.

It's a common 'issue' with the MINI (more widely, BMW's in general). Apparently it's actual company policy to make the speedometer read higher than reality on purpose to discourage speeding. Although I've read that the odometer uses different sensors, which give a more accurate reading, as to not screw up mileage.

I'll be ditching my OEM wheels/tires for aftermarket ones with a slightly larger diameter (215/45/17) next month. That should correct the error just a bit as well as helping out my wheel gap (in a similarly miniscule fashion) until I get lowering springs installed come Spring.