Conclusions. We confirm that AGN IR-selection is genuinely biased towards unobscured AGNe, but only at intermediate luminosities. At the highest luminosities, where AGN IR-selection is more efficient, there is no obscuration bias. We show that type-1 AGNe are intrinsically more luminous than type-2 AGNe only at z less than or similar to 1.6, thus resulting in more type-1 AGN being selected when the IR survey is shallower. Based on this and other studies, we conclude that deep hard-X-ray coverages, high-resolution IR imaging, or a combination of IR and radio data are required to recover the lower luminosity obscured AGN population. In addition, wide IR surveys are needed to recover the rare powerful, obscured AGN population. Finally, when the James Webb Space Telescope comes online, the broad-band filters 2.0 mu m, 4.4 mu m, 7.7 mu m, and 18 mu m will be essential for disentangling AGN from non-AGN dominated SEDs at depths where spectroscopy becomes impractical.