I've recently been researching metals for unrelated D&D purposes. Apparently, although steel is all kinds of awesome, pure wrought iron is ridiculously soft. The only reason Iron outstripped Bronze IRL is because the ancients ran out of tin, and iron was convenient and widely available. There are accounts from Roman soldiers who fought the Gauls, who were using iron weapons, and supposedly during breaks in the battle the Gauls would have to bend their swords back in shape.
Its still probably harder than gold, but the comparison isn't far-fetched assuming Dwarves are the only ones with Steelmaking technology. Although interestingly, in this scenario the world we look at isn't medieval fantasy, but Bronze Age fantasy.
Probably harder than gold? Heheh... Gold is super soft. Gold has the hardness of a fingernail. You can actually make an indent in pure gold just by pressing your fingernail into it hard enough. This is why they alloy it with copper and silver and such when making jewelry - its just so darn soft and not practical when pure.
Iron, on the other hand, is quite a bit harder. Sure, it will bend when made into a sword and beat against something (better to bend than break), but so will bronze. Quality bronze vs quality iron using iron-age processes would probably be pretty similar, since the forging process added some level of carbon to the iron anyway (heating in coals, hammering flecks of said coals into metal, etc). A gold long sword would probably bend under its own weight.
Also, I'm no metallurgy expert, but isn't "pure" wrought iron kind of nonsensical? I thought wrought iron was impure iron by definition (slag and other impurities from the smelting process). I don't think that's the kind of iron they used to make things like swords, since the impurities would make it too weak.