In this paper we develop statistical methods to compare two independent samples of multivariate functional data that differ in terms of covariance operators. In particular we generalize the concept of depth measure to this kind of data, exploiting the role of the covariance operators in weighting the components that define the depth. Two simulation studies are carried out to validate the robustness of the proposed methods and to test their effectiveness in some settings of interest. We present an application to Electrocardiographic (ECG) signals aimed at comparing physiological subjects and patients affected by Left Bundle Branch Block. The proposed depth measures computed on data are then used to perform a nonparametric comparison test among these two populations. They are also introduced into a generalized regression model aimed at classifying the ECG signals.