Understanding and modeling mortality patterns, particularly differences in death between populations, is crucial for demographic analysis and public health planning. In this study, we compare three statistical models in the Age-Period context to analyse differences in death counts. The models considered are based on Double Poisson, Bivariate Poisson, and Skellam distributions, each offering distinct advantages in capturing the underlying mortality trends. Using mortality data spanning from 2003 to 2020 related to the two major causes of death in Italy: cancer and diseases of the circulatory system, our analysis reveals significant temporal and age-related variations in the mortality patterns of the two causes. We find that the Skellam distribution model, while a novel approach in this field, demonstrates superior accuracy and simplicity in capturing mortality differentials. Our findings underscore the potential utility of the Skellam distribution in mortality gaps analysis.