In resource-limited or point-of-care settings, rapid diagnostic tests (RDTs), that aim to simultaneously detect HIV antibodies and p24 capsid (p24CA) antigen with high sensitivity, can pose important alternatives to screen for early infections. We evaluated the performance of the antibody and antigen components of the old and novel version of the Determine™ HIV-1/2 Ag/Ab Combo RDTs in parallel to quantifications in a fourth-generation antigen/antibody immunoassay (4G-EIA), p24CA antigen immunoassay (p24CA-EIA), immunoblots, and nucleic acid quantification. We included plasma samples of acute, treatment-naïve HIV-1 infections (Fiebig stages I–VI, subtypes A1, B, C, F, CRF02_AG, CRF02_AE, URF) or chronic HIV-1 and HIV-2 infections. The tests’ antigen component was evaluated also for a panel of subtype B HIV-1 transmitted/founder (T/F) viruses, HIV-2 strains and HIV-2 primary isolates. Furthermore, we assessed the analytical sensitivity of the RDTs to detect p24CA using a highly purified HIV-1NL4-3 p24CA standard. We found that 77% of plasma samples from acutely infected, immunoblot-negative HIV-1 patients in Fiebig stages II–III were identified by the new RDT, while only 25% scored positive in the old RDT. Both RDTs reacted to all samples from chronically HIV-1-infected and acutely HIV-1-infected patients with positive immunoblots. All specimens from chronically infected HIV-2 patients scored positive in the new RDT. Of note, the sensitivity of the RDTs to detect recombinant p24CA from a subtype B virus ranged between 50 and 200 pg/mL, mirrored also by the detection of HIV-1 T/F viruses only at antigen concentrations tenfold higher than suggested by the manufacturer. The RTD failed to recognize any of the HIV-2 viruses tested. Our results indicate that the new version of the Determine™ HIV-1/2 Ag/Ab Combo displays an increased sensitivity to detect HIV-1 p24CA-positive, immunoblot-negative plasma samples compared to the precursor version. The sensitivity of 4G-EIA and p24CA-EIA to detect the major structural HIV antigen, and thus to diagnose acute infections prior to seroconversion, is still superior.