We assess the dependence of magnetic exchange couplings on the variation of Hartree-Fock exchange (HFX) admixture in global hybrid functionals and the range-separation parameter in range-separated hybrid functionals in a set of 12 spin-1/2 binuclear transition metal complexes. The global hybrid PBEh (hybrid Perdew-Burke-Ernzerhof) and range-separated hybrids HSE (Heyd-Scuseria- Ernzerhof) and LC-PBE (long-range corrected hybrid PBE) are employed for this assessment, and exchange couplings are calculated from energy differences within the framework of the spin-projected approach. It is found that these functionals perform optimally for magnetic exchange couplings with 35 HFX admixture for PBEh, 0.50 a.u. -1 for LC-PBE, and at or near 0.0 a.u. -1 for HSE (which corresponds to PBEh). We find that in their standard respective forms, LC-PBE slightly outperforms PBEh, while PBEh with 35 HFX yields exchange couplings closer to experiment than those of LC-PBE with 0.50 a.u. -1. Additionally, we show that the profile of exchange couplings with respect to in HSE is appreciably flat from 0 to 0.2 a.u. -1. This combined with the fact that HSE is computationally more tractable than global hybrids makes HSE an attractive alternative for the evaluation of exchange couplings in extended systems. These results are rationalized with respect to how varying the parameters within these functionals affects the delocalization of the magnetic orbitals, and conclusions are made regarding the relative importance of range separation versus global mixing of HFX for the calculation of exchange couplings.