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Hunter is right...I guess in theory since you are sitting on the driver side, the passenger rear might have a bit less weight on it, and therefore less grip, but if the driver rear is sitting in puddle or on some sand or oil, it will be the one to break loose. The differential doesn't favor one side or the other, everything else being equal.
if you're on dry pavement, normally the passenger rear will spin. but if the driver side tire is like on ice or something it will spin. open diffs are stupid, which is why im going to be swapping mine to an auburn LSD in the spring.