The emergence of several SARS-CoV-2 variants has caused global concerns about increased transmissibility, increased pathogenicity, and decreased efficacy of medical countermeasures. Animal models can be used to assess phenotypical changes in the absence of confounding factors. Here, we compared variants of concern (VOC) B.1.1.7 and B.1.351 to a recent B.1 SARS-CoV-2 isolate containing the D614G spike substitution in the rhesus macaque model. B.1.1.7 behaved similarly to D614G with respect to clinical disease and replication in the respiratory tract. Inoculation with B.1.351 resulted in lower clinical scores, lower lung virus titers, and less severe lung lesions. In bronchoalveolar lavages, cytokines and chemokines were up-regulated on day 4 in animals inoculated with D614G and B.1.1.7 but not with B.1.351. In nasal samples, cytokines and chemokines were up-regulated only in the B.1.1.7-inoculated animals. Together, our study suggests that circulation under diverse evolutionary pressures favors transmissibility and immune evasion rather than increased pathogenicity.