Differential expression analysis of single-cell RNA sequencing (scRNA-seq) data is central for characterizing how experimental factors affect the distribution of gene expression. However, distinguishing between biological and technical sources of cell-cell variability and assessing the statistical significance of quantitative comparisons between cell groups remain challenging. We introduce Memento, a tool for robust and efficient differential analysis of mean expression, variability, and gene correlation from scRNA-seq data, scalable to millions of cells and thousands of samples. We applied Memento to 70,000 tracheal epithelial cells to identify interferon-responsive genes, 160,000 CRISPR-Cas9 perturbed Tcells to reconstruct gene-regulatory networks, 1.2 million peripheral blood mononuclear cells (PBMCs) to map cell-type-specific quantitative trait loci (QTLs), and the 50-million-cell CELLxGENE Discover corpus to compare arbitrary cell groups. In all cases, Memento identified more significant and reproducible differences in mean expression compared with existing methods. It also identified differences in variability and gene correlation that suggest distinct transcriptional regulation mechanisms imparted by perturbations.