Degenerate hydrogen atom exchange reactions have been studied using calculations, based on density functional theory (DFT), for (i) benzyl radical plus toluene, (ii) phenoxyl radical plus phenol, and (iii) methoxyl radical plus methanol. The first and third reactions occur via hydrogen atom transfer (HAT) mechanisms. The transition structure (TS) for benzyl/toluene hydrogen exchange has C-2h symmetry and corresponds to the approach of the 2p-pi orbital on the benzylic carbon of the radical to a benzylic hydrogen of toluene. In this TS, and in the similar C-2 TS for methoxyl/methanol hydrogen exchange, the SOMO has significant density in atomic orbitals that lie along the C-H vectors in the former reaction and nearly along the O-H vectors in the latter. In contrast, the SOMO at the phenoxyl/phenol TS is a pi symmetry orbital within each of the C6H5O units, involving 2p atomic orbitals on the oxygen atoms that are essentially orthogonal to the O...H...O vector. The transferring hydrogen in this reaction is a proton that is part of a typical hydrogen bond, involving a sigma lone pair on the oxygen of the phenoxyl radical and the O-H bond of phenol. Because the proton is transferred between oxygen a orbitals, and the electron is transferred between oxygen pi orbitals, this reaction should be described as a proton-coupled electron transfer (PCET). The PCET mechanism requires the formation of a hydrogen bond, and so is not available for benzyl/toluene exchange. The preference for phenoxyl/phenol to occur by PCET while methoxyl/methanol exchange occurs by HAT is traced to the greater pi donating ability of phenyl over methyl. This results in greater electron density on the oxygens in the PCET transition structure for phenoxyl/phenol, as compared to the PCET hilltop for methoxyl/methanol, and the greater electron density on the oxygens selectively stabilizes the phenoxyl/phenol TS by providing a larger binding energy of the transferring proton.