It was actually stated by Blizzard at some point that the difficulty does matter (the higher diff, the better chance), though of course it's unclear as to how much it matters exactly. From what I remember back in 8.0 and 8.1 the general consensus was to run normals, because mythics were really hard back then. Now this is no longer so though, and the speed of clearing is pretty much the same in a geared group, so there's no reason to run anything below mythic if you're going for mounts. Plus you get way more dubloons on mythic (average of 11-12 per island).
I run about 300+ mythic islands in 8.2, and received 0 mounts, so they must have tweaked the rates up, or I'm having some crazy insane luck in 8.3 all of a sudden.