Deep profiling of cell states can provide a broad picture of biological changes that occur in disease, mutation, or in response to drug or chemical treatments. Morphological and gene expression profiling, for example, can cost-effectively capture thousands of features in thousands of samples across perturbations, but it is unclear to what extent the two modalities capture overlapping versus complementary mechanistic information. Here, using both the L1000 and Cell Painting assays to profile gene expression and cell morphology, respectively, we perturb A549 lung cancer cells with 1,327 small molecules from the Drug Repurposing Hub across six doses. We determine that the two assays capture some shared and some complementary information in mapping cell state. We find that as compared to L1000, Cell Painting captures a higher proportion of reproducible compounds and has more diverse samples, but measures fewer distinct groups of features. In an unsupervised analysis, Cell Painting grouped more compound mechanisms of action (MOA) whereas in a supervised deep learning analysis, L1000 predicted more MOAs. In general, the two assays together provide a complementary view of drug mechanisms for follow up analyses. Our analyses answer fundamental biological questions comparing the two biological modalities and, given the numerous applications of profiling in biology, provide guidance for planning experiments that profile cells for detecting distinct cell types, disease phenotypes, and response to chemical or genetic perturbations.