HIV-infected individuals under antiretroviral therapy often have a compromised HIV-specific T cell immune response due to the lack of CD4 T cell help, viral escape, T cell exhaustion, and reduction in cell numbers due to the withdrawal of cognate antigen. A successful HIV cure strategy will involve a durable and potent force that can effectively recognize and eliminate remaining virus that may emerge from latency months, years, or perhaps decades after an individual undergoes an HIV cure regimen. T cells are ideally suited to serve in this role, but given the state of the HIV-specific T cell response, it is unclear how to best restore HIV-specific T cell activity. To compare the efficacy of TCR and CAR T cell strategies we generated engineered T cells using lentiviral vectors encoding one of three distinct HIV-specific T cell receptors (TCRs) or a previously optimized HIV-targeting chimeric antigen receptor (CAR) and compared their functional capabilities. All engineered T cells had robust, antigen-specific polyfunctional cytokine profiles when mixed with artificial antigen-presenting cells. However, only the CAR T cells could potently control HIV replication. TCR affinity enhancement did not augment HIV control but did allow TCR T cells to recognize common HIV escape variants. Interestingly, either altering Nef activity or adding additional target epitopes into the HIV genome bolstered TCR T cell anti-HIV activity, but CAR T cells remained superior in their ability to control HIV replication. To better understand why CAR T cells, control HIV replication better than TCR T cells, we performed a time course to determine when HIV-specific T cells were first able to activate Caspase 3 in HIV-infected targets. We demonstrated that CAR T cells recognized and killed HIV-infected targets more rapidly than TCR T cells, which correlates with their ability to control HIV replication. These studies suggest that the speed of target recognition and killing is a key determinant of whether engineered T cell therapies will be effective against infectious diseases.