Cellular omics such as single-cell genomics, proteomics, and microbiomics allow the characterization of tissue and microbial community composition, which can be compared between conditions to identify biological drivers. This strategy has been critical to revealing markers of disease progression, such as cancer and pathogen infection. A dedicated statistical method for differential variability analysis is lacking for cellular omics data, and existing methods for differential composition analysis do not model some compositional data properties, suggesting there is room to improve model performance. Here, we introduce sccomp, a method for differential composition and variability analyses that jointly models data count distribution, compositionality, group-specific variability, and proportion mean–variability association, being aware of outliers. sccomp provides a comprehensive analysis framework that offers realistic data simulation and cross-study knowledge transfer. Here, we demonstrate that mean–variability association is ubiquitous across technologies, highlighting the inadequacy of the very popular Dirichlet-multinomial distribution. We show that sccomp accurately fits experimental data, significantly improving performance over state-of-the-art algorithms. Using sccomp, we identified differential constraints and composition in the microenvironment of primary breast cancer.