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as little as possible if you are going to run it on any dru or hard ppack surface, that is provided you are running the same size tires front, and rear.
Some of the mud guys run different diameter tires with equal gear ratios, and some rune the same size tire with different ratios. I guess application has much to do with what you could get away with, if traction permits. A t- case will give snap, crackle, and pop in a nig hurry if you run the front, and rear at different speed, with any type of traction.
The only stock application I can think of that actually has a difference is with 4.10 on one end and 4.11 on the other, though I can't think of the vehicle that uses it.
I can't put any numbers to it, but I remember there being other applications where there is a slight difference as well. With most 4x4's having different front and rear axles, it is not always possible to get exact matches in ratios. It seems that at least a 100th difference front to rear is tolerable.
Probably does not matter at this point, but I forgot about transfer case differentials, like the one found in the np203. This is designed to allow the front axles to turn at a different rate than the rear, so a big difference in ratios could be allowable, but still would find no practical reasons behind running a different gear from front to rear.