We apply the density functional theory + U (DFT+U) and unrestricted hybrid functional DFT-UB3LYP methods to study the electronic structure and magnetic properties of two prototypical iron porphines: iron(III) porphine chloride (FePCl) and difluoro iron(III-IV) porphine. Plain DFT within the generalized gradient approximation (GGA) implementation fails in describing the correct high-spin ground state of these porphine molecules, whereas DFT+U and UB3LYP provide an improved description. For a range of U values (4-8 eV), we compare the results of the DFT+U approach to those obtained previously with the hybrid functional (B3LYP) and with the CASPT2 approach. The DFT+U and UB3LYP methods successfully predict the molecular high spin (S = 5/2) ground state of FePCl, and also provide the nontrivial S = 3 high spin ground state for FePF(2). For the latter six-coordinated Fe porphine, our DFT+U calculations show that the S = 2, S = 5/2, and S = 3 states are energetically very close together (differences of 30 meV). Nonetheless, S = 3 is obtained as the ground state of the whole molecule, in accordance with the spin expected from the electron count. Our DFT+U calculations show furthermore that the Fe 3d occupancy is similar for FePF(2) and FePCl, i.e., DFT+U does not support Fe(IV) for FePF(2), but rather an Fe(III) porphyrin π-cation radical species, with an Fe high spin S(Fe) = 5/2, and an additional S = 1/2 stemming from spin density distributed over the porphine ring. This observation is also supported by our UB3LYP calculations.