For the history: I leveled using a dual spec of Protection and Fury. Well... just Fury, really, because Protection is nice, but during leveling I want to kill things fast. I started leveling on the 8th of December 2010 and there was not very much information available yet. While leveling I heard time and time again that the new Arms tree was fun and competitive DPS.
I did play my first few instances at maximum level as Fury - with a spec pretty much identical to this (First post, headed - surprisingly - Fury). And I have to say I was happy with my DPS. It was certainly comparable to what other specs put out, sometimes even slightly ahead. Fury also has the enormous advantage of having a rotation built around Bloodthirst - and thus a self-heal. This means as long as you only rarely take damage, you'll eventually be topped up again. Even if the healers have to conserve their mana and ignore DPS in no imminent danger of death.
Luckily, I began reading the arms dps thread on Elitist Jerks. Somewhere (post 99, basically) is a compilation of damage results for arms - with a link to a simulator.
Now, if you can get the simulator to import your profile from the armoury (and by default it's set to the US version - some fiddling required) will provide damage results for an imaginary boss fight of 5 minutes length. And more importantly - it works for a large variety of specs (and classes).
My first results (and that is not in the gear I wear now - at the time of "decision making") were quite surprising. Apparently Arms seriously outperformed Fury with my gear. The theoretical DPS jumped from approximately 8500dps to 10300dps (let's not discuss how theoretical dps coincides with my results).
And much like the Battlemaiden of this questline, arms has the advantage of bringing Charge, Rend, Sweeping Strikes and
So .. to finish with the prattling .. according to my theorycrafting (well, someone elses - my use of the simulator) Arms currently outperforms Fury for DPS. This will likely change over time and with better gear, unless the specs are better balanced than they were in the past.
What spec to use, then?
My suggestion deviates slightly from Our Girl Friday and the Elitist Jerks suggestions. I'd go for something like this for instances and heroic instances. There are several options really. The improved damage for Slam (Improved Slam, Arms tier 4) is a bit pointless and you can relocate those to Second Wind, Blitz or even Improved Hamstring. The points in Rude Interruption (Fury, tier 2) could go into Executioner instead - but I found most bosses in heroics do not live long enough to get the speed bonus more than twice. Incite (Protection, tier 1) is also negotiable and could easily turn into Blood and Thunder if you wanted more AoE damage.
And the rotation?
Well, get as much rage as you can before the pull (Battleshout, Glyphed Bloodrage, beating up a lurking tempest) and wait for your tank to position the enemy where he wants to fight them. Charge and apply rend to your primary target. After that, hit your abilities in the priority order of:
Colossus Smash, Mortal Strike, Overpower.
Make sure Rend gets reapplied as soon as it drops off (try not to clip at - I still fail at this) and use any excess rage for Heroic Strikes or Cleaves.
The amount of damage (and threat) is quite impressive.
One additional note: Heroic Leap (while good fun) is not a good ability to initiate combat with. It generates no rage and will leave your dps falling behind at the beginning - which is not made up for by the paltry damage the landing does. It is, however, an amazing ability to get away from bad stuff. Especially as it's targetted (and allows you to get away from Asaads Supremacy of the Storm at the last second for instance). Just keep in mind it requires a global cooldown.