For small N, Pearson’s correlation coefficient has an advantage over logistic regression. One can compute the permutation distribution of Pearson’s correlation coefficient exactly. For the exact distribution, true type I error is equal to nominal type I error. Such won’t be the case for logistic. Also, I bet it’s more powerful than logistic for small N. One could do some simulations and look at this—it’s a good master’s paper project, perhaps. This is the case where Pearson’s correlation coefficient is a better choice than logistic regression or other regression modeling.