Uebersax (1987), Hutchison (1993) and Bonnet and Price (2005) each compare Kappa and Correlation and conclude that there does not seem to be any situation where Kappa would be preferable to Correlation.
all the Kappa and Correlation variants considered were symmetric, and it is thus interesting to consider the separate regression coefficients underlying it that represent the Powers Kappa duals of Informedness and Markedness, which have the advantage of separating out the influences of Prevalence and Bias (which then allows macroaveraging, which is not admissable for any symmetric form of Correlation or Kappa, as we will discuss shortly).