rtist
Externally/deleted/jacknived studentized residuals are generally preferred, esp. when the computation can be easily done without repeated fitting of models, because if the point is influential, it's affecting not only the coefficients, but also the variance estimate. Another advantage of external studentization is that theoretical distribution can usually be derived analytically.
Cook's distance measures the influence on overall coefficients of the model; (externally) studentized residuals reflect the influence on the fit for a point only.