This paper compares the performance of two new directionally-sensitive multivariate methods, based on the multivariate CUSUM (MCUSUM) and the multivariate exponentially weighted moving average (MEWMA), for biosurveillance. While neither of these methods is currently in use in a biosurveillance system, they are among the most promising multivariate methods for this application. Our analysis is based on a detailed series of simulations using synthetic biosurveillance data that mimics various types of disease background incidence and outbreaks. We apply the MCUSUM and the MEWMA to residuals from an adaptive regression that accounts for the systematic effects normally present in biosurveillance data. We find that, much like the results from univariate CUSUM and EWMA comparisons in classical statistical process control applications, the directionally-sensitive MCUSUM and MEWMA perform very similarly.