Ok, well since I seem to be the only one here who's an avid Hunter fan (I had a level 54, 32, 23 and 21) I'll let you know how it really boils down.
First off, Hunters are first and foremost solo artists. There's an argument over who's better, Warlocks vs. Hunters, but putting that aside it's not hard to see how much a Hunter stands above the rest when it comes to solo'ing. Other classes can solo, sure. But not with the efficiency at which a Hunter solo's. No where NEAR a Hunter's efficiency.
We're not that terribly great in PvP though. At least on our own. Mostly because our pets are just blatantly ignored and we get rushed by the melee's cutting off our ranged weaponry and leaving us to our melee abilities. And quite honestly, we're not made for melee. Sure we can do a little bit. We're not helpless. But we're not even in the same league as a Warrior, Paladin or, more importantly, a rogue.
But we bring alot to the table in PvP groups. We don't always hit as hard as Mages do but we hit faster and longer which makes us a prime canidate for artilary. And not to mention our ability to flush out Stealthed Druids and Rogues. Man do they really hate our guts. Nothing like sneaking up on a target just to realise there's a BIG RED flashing arrow over your head marking you for the world to see. That drives 'em bonkers. Toss in our Aspect of the Pack (the only group run buff in the game) and a Hunter is always a welcome addition to any PvP party.
And as far as how much damage we put out? Lemme put it to you this way. My pets can solo... that's right solo... creatures two levels lower then it without going beyond 3/4 it's health. Now that should give you some idea of how much damage a pet can do. That alone speaks volumes as to the damage output of which a Hunter provides. Your pet crits I would have to say at least once or twice a fight and you (post 25) will be critting about the same frequency. Combine that with the phenomenal regeneration rate of your pets... *whistles*
Alot of people just don't truly understand the damage output that a Hunter gives out. There's a reason we don't get much of a crit/dmg increase on our ranged weaponry via talents. Unlike Rogues for instance. Now of course a Hunter can't pump out the crazy crits like a Rogue or Warrior can but bear in mind that 1.) The infamous warrior crit (12k+) only activates when the target is down to 20% health. Highly situational. Really only useful for taking nifty screenshots to brag about and 2.) Rogues don't put out as many of those high crits that you might think they do. That's not to say that neither a rogue or a warrior are hard core opponents. Quite the opposite. Just don't base your opinion on 'em based solely on statistical information which occurs post lvl 55 and only on seldom occassions.
As far as Dueling? I wouldn't expect to be "owning" any melee classes anytime soon. The only class a Hunter has a distinct advantage on in regards to dueling is a Mage. Hands down. Whenever I'd get challenged by a mage I'd give him a choice. I'll not use my pet if you don't use your polymorph. If he said no. Fine. His loss. He'll get his poly off for sure but not before he's been driven down to 1/2 - 1/3 his health at which time my pet would either own him or he would focus on trying to get rid of my pet at which time I would get out and he would either be dead or about to die. Or he would accept the no poly/no pet agreement and he would go down anyway. Mages put out some good damage but not as fast as we can and we don't have to worry about casting delays like they do.
All in all a Hunter isn't something to be trifled with. We put out really good damage at a solid and consistant rate. Whereas others might put out more damage but not as solid nor as consistant, such as a rogue/warrior.
Pally's aren't even in the same ballpark. They have a completely different purpose so there's no real reason to compare the two. That's like saying a hammer is better then a screwdriver. Depends on the job intended.