OSI and Pearson's 2 coefficient are zero when average equals median.
OSI and Pearson's 2 coefficient are invariant when the data set is multiplied by a constant factor.
OSI but not Pearson's 2 coefficient correlates with the coefficient of variation (average/SD) when the data set is baseline corrected by a constant factor. OSI changes after a data set is baseline corrected by a constant factor, which changes x at a given SD. This does not affect Pearson's 2 index.
OSI changes from flux control ratio Y/Z to flux control efficiency 1-Y/Z, which changes x at a given SD. This does not affect Pearson's 2 index. In both cases the sign is changed.