I've got to say I prefer Elric. So I'm disappointed that his early lead has been crushed by the Conan-philes.
While reading the REH tales I found it really hard to get past the casual chauvinism, misogyny and racism. I'm glad I read them; the tropes of lost cities, evil sorcerers, and treasure hunts, really stand out as a real influence on D&D and are cool. But Conan isn't really an admirable character, none of the tales have much in the way of complexity, I also get tired of Conan routinely dismembering villains with a single sword thrust. Howard waxing lyrical about the barbarian's physical prowess gets grating, and the word "thews" is overused.
As for Elric. As has been pointed out, his world is a bit strange - much of the "normal" fantasy setup isn't there so there is stuff that's odd. Though you can see the D&D in Law/Chaos and elementals. I think Elric with his moral sensibilities, his weakness, together with his sorcery and Stormbringer make him a really complex and interesting character than Conan. I also think the way magic is done in Elric - calling on ancient pacts with Demonic and Elemental beings - is really interesting and unique. It's a shame more of this didn't get into D&D. I can see why it didn't (you want the PCs to have the power, not monsters they call); but it'd still be cool if I could get Arioch to help my PC out.