For starters, let me say that I think this is one of those loaded topics. Starting a "Conan or Iron Heroes" thread is a bit like starting a "D&D or Castles & Crusades" thread. Some people believe that the only way for one system to triumph is for the other to be laid low.
Now, from my perspective, I haven't played Conan, though I thumbed through it at the store, but I bought IH before it was in print. I'd suggest that one's preference for one system over the other would hinge on your answer to the following questions.
1) How rules savvy are your players? If their rules-fu is good, IH is fine. If they leave all the work to the DM, go with Conan.
2) Do the players just want "action fantasy without magic items" or do they want "action fantasy where they could be killed at any moment?" The ability to be killed by a mook may be "realistic," but without some kind of plot protection (does Conan use something like action points?), it can be thoroughly unsatisfying to lose a good character to nothing but bad luck. Iron Heroes characters have a fair amount of plot protection (in the form of high hit points). Yes, the loss of active defense sucks, but you can do a fair amount to shield yourself from that happening...and if you don't, well, that's more than just bad luck.
3) How open are the players to new systems? Iron Heroes uses a lot of new mechanics, Conan fewer. Some people think D&D is too complicated (magic aside). I don't mind D&D, other than the magic item complexity.
A few things to bear in mind:
Iron Heroes is, to a certain extent, as much toolkit as game. Skill groups port nicely to other systems, allowing more capable characters. Stunts, skill challenges, and zones port even more easily. And they add a LOT to the game. Learning how they work is really simple, and they do a nice job of making combat (much) more interesting.
I actually prefer tokens to "per day" abilities, because they allow you to run multiple encounters in a day without fear of killing PCs. That can lend to a "breakneck speed" feel IN-GAME. They're also very easy to keep track of, and for all but the most mystical character abilities, they feel much more realistic. Where I personally feel IH fell short is in not "finishing the job" by making spellcasters work on similar mechanics. Now, that's probably because spellcasting isn't Mike Mearls' design specialty, but that Monte Cook guy has designed a spell or two in his day...
Now if we could just get a hit point system that worked better. I'm thinking something like WP/VP without the added random lethality.