Distinction between Kendall's tau and Spearman's rho comes from dependence structure that they measure. While the first one is a metric of average likelihood ratio dependence, the latter one focuses on measuring average quadrant dependence [2].
2.2.3. Coefficients of Tail dependence
If the subject of concern is the joint behavior of two random variables in the tails of the distributions, then coefficients of upper and lower tail dependence must be analyzed.