Differential expression analysis of scRNA-seq data is central for characterizing how experimental factors affect the distribution of gene expression. However, it remains challenging to distinguish biological and technical sources of cell-cell variability and to assess the statistical significance of quantitative comparisons between groups of cells. We introduce memento to address these limitations and enable accurate and efficient differential expression analysis of the mean, variability, and gene correlation from scRNA-seq. We used memento to analyze 70,000 tracheal epithelial cells to identify interferon response genes with distinct variability and correlation patterns, 160,000 T cells perturbed with CRISPR-Cas9 to reconstruct gene-regulatory networks that control T cell activation, and 1.2 million PMBCs to map cell-type-specific cis expression quantitative trait loci (eQTLs). In all cases, memento identified more significant and reproducible differences in mean expression but also identified differences in variability and gene correlation that suggest distinct modes of transcriptional regulation imparted by cytokines, genetic perturbations, and natural genetic variation. These results demonstrate memento as a first-in-class method for the quantitative comparisons of scRNA-seq data scalable to millions of cells and thousands of samples.