I'll lead off with a thought or two:
"Easier to DM" is a rather iffy notion. IH, for example, features much more complexity of combat than Conan, because of the many and varied class abilities, the feat mastery system, the extensive use of token abilities, and the stunts and zones. On some level, combat is SUPPOSED to be complex in IH; it's designed to encourage and accommodate as many cinematic maneuvers as possible. Combat in Conan is a bit more... er, direct. The maneuvers are far fewer, more limited, and more straightforward, and the body count (either mooks or PCs!) is likely to mount up too fast for there to be much running around or making arrow ladders or such. OTOH, IH is designed to be balanced with D&D CRs and general adventure design. Thus, IH characters are easier to run in published modules, etc than are Conan characters.
Conan is, IMHO, generally simpler than IH if one judges by the simple criterion of page count. The classes have a limited (IMHO, rather bland) set of abilities, except for the Noble and the Scholar, whose capabilities require some careful DM and player research to fully understand. Skills, feats, and the combat system don't require a lot of reading to grasp.
The reasons that Conan might be better than IH are conditional, IMHO:
1) If you run a Hyborian campaign. Er, no question here. Conan has the races, the flavor, etc., and the classes and combat system are written with running a nice, grim, bloody Conanesque adventure set in mind.
2) If you want something a bit lower on the power curve, or generally a bit more "gritty" (gods, I hate that word!). High-level Conan PCs have far fewer hit points than their D&D/IH counterparts, weapons do more damage, and there's no magical gear floating around. Plus, combat against multiple mooks is substantially more deadly. Add all these things together, and it means a world in which PCs are much more likely to die than one in which IH is the default ruleset. Keep in mind that IH PCs are just as powerful as D&D PCs; they just use innate abilities and skills, rather than magic, to get there. Conan PCs (or, IIRC, Grim Tales PCs) are simply NOT as powerful as D&D PCs. Prick them, they bleed, etc.