Mismatching tires on Four Wheel Drive and All Wheel Drive vehicles can cause damage to the front or rear differentials and or transfer cases. So when replacing tires on these vehicles it is recommended to replace all four tires at the same time. Any thing over 1/2 of an inch difference in the tire height can cause problems.
Limited Slip Differentials have clutches that are designed to engage if one wheel basically spins faster than the other to help maintain traction, so if one tire is smaller than the other the smaller tire will spin faster and the clutches will stay engaged all the time. This would cause damage to the differential in a short amount of time.
The Automatic Four Wheel Drive and the All Wheel Drive systems will also be effected by this. On the Automatic Four Wheel Drive system the on board computer reads the wheel speed sensors located at each wheel. If it sees a certain difference in wheel speeds it interprets this to be a loss of traction and engages the transfer case. If driven for prolong period of time on asphalt this will burn up the transfer case. All Wheel Drive system use what is called a Vicious Coupler. This is a unit inside the transfer case that has a special fluid inside it that when it heats up will engage the transfer case. If one wheel is spinning faster than the other then this will cause the coupler to engage and can cause damage if driven for prolong period of time. So if replacing tires on these vehicles do not try to replace two tires and get that extra mileage out of the other two. If you only replace one or two tires make sure to measure the circumference of the tires to make sure they are within 1/2 inch. We had a vehicle in our shop once that had two tires replaced with same size and brand just the two older tires were three years older, and there was one inch difference in the height. Tires although they can be expensive are a lot cheaper than repairing or replacing the differential or transfer case.