The development of an effective human immunodeficiency virus (HIV-1) vaccine is a high global health priority. Soluble native-like HIV-1 envelope glycoprotein trimers (Env), including those based on the SOSIP design, have shown promise as vaccine candidates by inducing neutralizing antibody responses against the autologous virus in animal models. However, to overcome HIV-1's extreme diversity a vaccine needs to induce broadly neutralizing antibodies (bNAbs). Such bNAbs can protect non-human primates (NHPs) and humans from infection. The prototypic BG505 SOSIP.664 immunogen is based on the BG505 env sequence isolated from an HIV-1-infected infant from Kenya who developed a bNAb response. Studying bNAb development during natural HIV-1 infection can inform vaccine design, however, it is unclear to what extent vaccine-induced antibody responses to Env are comparable to those induced by natural infection. Here, we compared Env antibody responses in BG505 SOSIP-immunized NHPs with those in BG505 SHIV-infected NHPs, by analyzing monoclonal antibodies (mAbs). We observed three major differences between BG505 SOSIP immunization and BG505 SHIV infection. First, SHIV infection resulted in more clonal expansion and less antibody diversity compared to SOSIP immunization, likely because of higher and/or prolonged antigenic stimulation and increased antigen diversity during infection. Second, while we retrieved comparatively fewer neutralizing mAbs (NAbs) from SOSIP-immunized animals, these NAbs targeted more diverse epitopes compared to NAbs from SHIV-infected animals. However, none of the NAbs, either elicited by vaccination or infection, showed any breadth. Finally, SOSIP immunization elicited antibodies against the base of the trimer, while infection did not, consistent with the base being placed onto the virus membrane in the latter setting. Together these data provide new insights into the antibody response against BG505 Env during infection and immunization and limitations that need to be overcome to induce better responses after vaccination.