Generally in PvE, a fury build or a fury/arms build will significantly outdamage an arms or arms/fury build. Since the changes to warrior talents with the release of The Burning Crusade, a Fury/Protection build is viable for offtanking but will produce less raw damage than fury/arms. The fury tree is mostly built around the talents Flurry and Enrage (although in an instance, hopefully your DPS warrior would not be getting hit as often, so Enrage will not be active as much) although the former top talent is Bloodthirst, an instant attack that scales with attack power, and the current top talent is Rampage, which like Flurry relies on the warrior striking a critical hit but like Retaliation and Overpower requires the warrior activate it when conditions are right.
Warriors can be very effective in the DPS role. Even with the changes to rage just before The Burning Crusade, a warrior who can generate enough rage and who has a high enough crit rating can enter into a state called 'Perma-Flurry' where their attack speed is increased almost indefinitely, allowing them to keep Rampage more or less constantly active as well. Bloodthirst, Heroic Strike and even Slam become rage dumps, allowing the warrior to maximize the use of his rage to deal damage. (Note: as posters have indicated, i did forget to mention that Heroic Strike is a high threat ability. It's prefereable to rage dump with Bloodthirst, Slam and Whirlwind if you don't have to be careful of CC.) The advantages to a warrior dealing damage over other classes are his higher armor (even if, as many do, he chooses to wear mail and leather damage pieces as they drop and are upgrades) and his ability to use any melee weapon in the game. The downside is a simple one - aside from Berserker Stance's inherent threat reduction, a warrior DPSing has no ability to shed hate aside from not doing damage. Every single warrior who has chosen to deal damage in raids and instances has had the experience of having the mob turn on him, and this can well lead to a dead warrior. Dead warriors do no DPS at all. Worse, if you pull aggro at the exact wrong moment, you can significantly hurt the entire raid or instance run.
But what about PvP, you ask? Why isn't this same strategy as effective there?
Well, generally in a raid (and yes, there are exceptions) the mobs can be crowd controlled or tanked, so the warrior in a damage dealing role can simply attack them. But in PvP, unless you get lucky, you're dealing with mobile targets who can and will do things like jump through you, use annoying abilities like Polymorph, Gouge, or Scattershot, or otherwise refuse to oblige you by letting you beat on them. Unlike a rogue, you can't so much to hold another player in place, and unlike a caster or hunter, you can't just stand in one place and damage them while they run around. While abilities like Hamstring and Piercing Howl can help even the odds, at the end of the day PvP calls for one thing from a warrior - giant freaking crits. Big critical hits are the way for a warrior to be as effective as possible in a setting where he's probably going to be rooted, feared (break the fear! Damn, they just sheeped me) or otherwise kept helpless as soon as people notice him.
Far, far better PvPers than me have assured me that the Arms/Fury spec is still incredibly viable for PvP. Some folks go 31 arms/30 fury, while others sing the praises of abilities like Second Wind, Improved Mortal Strike, and Endless Rage. You should experiment with builds on the test servers when you can (saves you the gold of a respec cost) and remember that you're a very gear dependent class. As you PvP more and earn gear upgrades, you'll most likely see improvements in your performance, but you're always going to be playing a warrior, which means you'll always see the most extreme highs and the most crushing lows when you're in there. Everyone will remember your massive MS crits and call for you to be nerfed. No one will remember when you spend 10 minutes stuck in one place and/or dead, unable to hit anyone and focus fired as soon as you come into view. Well, no one but you. Believe me, you'll remember it every time someone tells you that warriors are gods in PvP, and you'll laugh a very, very bitter laugh.
Warriors can be very devastating in PvP, don't worry. Especially if a paladin or druid adopts you. Properly buffed and healbotted (I still remember fondly the AV where a priest decided we were long lost brothers and just followed me everywhere I went) a warrior can wreak unholy havoc. Be sure to guard that healer's life - break off attacks on other targets to go after anyone who's trying to kill your immortality in a bottle, because you and a healer are worth far more than you would be without one.
As is usually the case, I've gone on way longer than I expected. Next time we'll look at builds for Tanking, DPSing and PvPing. Feel free to submit links to your own favorite builds in the comments here if you're a warrior looking to help out your fellows, or discuss the tricks you prefer to maximize your DPS and keep killing in PvP.