From an economic standpoint, it depends on how much you value grinding Hodir Dailies and how much you're willing to drop on Relics of Ulduar. If you absolutely despise the Hodir Area and want to just get exalted, you're looking at about 4680 Gold, assuming the relics go for 3g each. That's assuming you buy your way through. If you grind dailies, that goes down and gives you some cash as well.

If you're more interested in A shoulder enchant than the best one, getting honored is relatively cheap, 720 gold. Now, is leveling Inscription going to cost 5k? Not likely, and yes, you do get your shoulder enchant out of it without having to worry about all that silly Hodir stuff, at which point it becomes a matter of whether you have a free profesion slot and whether you want to spend it on inscription.

Personally, if you want the really good shoulder enchant, I don't see much difference time and gold wise between the two.