Arms is probably the best. I'm uncertain of either specc before you get colossus smash, but it feels like Arms is better at dishing out consistent damage. I leveled as Fury from 66 and onwards, though. I can't really stand Arms for some reason.
I leveled 70-90 as prot and between the insta dungeon queues and the large pulls to complete quests very quickly I was pretty much unstoppable with little to no downtime excluding the times I was very ambitious with my pulls
I don't think prot was ever the best leveling spec, tbh, unless you were leveling mainly through dungeons. That's when it's great, but prot's superiority was always more myth than fact. Arms and prot are both viable but arms is better at killing stuff quickly and both are able to easily survive very large pulls. Fury has changed since cata, when it comes to generating rage so can't really say. During cata the main problem was you didn't have the necessary gear and abilities to properly play fury at the lower end of the 1-60 level spectrum.
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I think the best spec for leveling depends on a few things.
1. Which heirlooms you have, or are willing to grind your current 90 to gain(if you have one)
2. If you are going to quest, do dungeons, PvP or some combination. I'm not sure which spec low-mid level warriors are using in BGs nowadays, and why.
3. Look at the different specs. Which specs get their differentiating special abilities and when? For instance, Fury Warriors don't have access to SMF or TG until 38. Arms Warriors don't get Taste for Blood until 50. When you have access to key abilities like these may have a great impact on your dps or quality of life.
4. If you're running dungeons, let the items do the talking. If you find two awesome 1-handed dps weapons, you might want to go SMF(Fury). If you find a brand new 2-hander that's quite a few ilevels above your current weapon(s), you might want to go Arms. However, if you end up simply loving Arms or Fury, just stick with the spec you like and the upgrades will come as you level.
5. If you love tanking, go Prot obviously.
As far as questing, it's a joke with any of the three. As Prot you will never die, but Arms and Fury will take down mobs quicker.
This is all great advice, thanks everyone. I should've mentioned I'm asking this question with the intention of leveling from 1-90. I'm starting fresh on a new server, so no heirloom items. I'm just wanting to get up there as quickly as possible. Since I'll mostly be questing, and Mitchell says it's a joke with all three, I think I feel a bit more secure about just doing whatever