FWIW, a quote from Myers & Well (research design and statistical analyses, second edition, 2003, p. 510). If you still care about the p-values;

> Seigel and Castellan (1988, nonparametric statistics for the behavioral sciences) point out that, although $\tau$ and Spearman $\rho$ will generally have different values when calculated for the same data set, when significance tests for $\tau$ and Spearman $\rho$ are based on their sampling distributions, they will yield the same _p_-values.