Accurate modeling of p-type dopants in 4H-SiC is essential for understanding the mechanisms governing doping efficiency and carrier transport. In this work, we revisit the electronic structure of boron- and aluminum-related acceptors using hybrid density functional methods. Besides defect formation energies and thermodynamic transition levels, we present a quantitative look into the carrier capture kinetics within the multi-phonon emission framework. Our results reveal striking differences between the two most relevant p-type dopants. While B_Si and B_C exhibit nearly identical formation energies, consistent with the occurrence of both defects, the formation energy of Al_C under intrinsic conditions is approximately 6.5 eV higher than that of Al_Si, confirming previous findings that the former is unlikely to occur. We further find that B_Si possesses large electron and hole capture cross sections, identifying it as a plausible source of minority-carrier lifetime degradation of n-type material contaminated with boron. In addition, we predict a previously unexplored donor transition for B_C. If experimentally confirmed, this defect would represent additional problems to both p-type doped and boron contaminated 4H-SiC, not only because of its ineffectiveness as an electric dopant, but also due to trapping of up to two free holes, reducing the free-hole concentration and increasing scattering effects.