Typically, a two handed weapon is mechanically more sound for multiple reasons.
One: The only real feat you need to invest in to get the damage going is Power Attack, anything after that is cake.
Two: The 1.5 damage you get going from one swing is a lot more than you get from one swing off of TWF. This is important when mobility and the availability of full attacks becomes increasingly important.
Three: Enchanting one weapon is a lot cheaper than enchanting two.
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Two-handed; it's hard enough to scale to hit often enough without taking -2 to all attacks. Also, mid-to-high staples that give extra attacks (a la haste) work better with two-handing; and with the manueverability of combat, having the vital strike "high damage output" keeps fighting-types much more viable.
Plus it's simply less feat-and-stat intensive. And it offers reach, which can yield several attacks as things come at you. Finally, even if both attacks hit on twf, it usually does about the same damage as one hit from a one-hander; why take the penalty?
I've always loved the flavor and stye of TWF. But these guys are right, THF is just mechanically superior/easier in most builds, tactics, and circumstances (though there are a few exceptions).
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Two Handed is the mechanically superior option in most cases. However there are some times where TWF can pull ahead. For Example, a Brawler fighter using Two Weapon Rend annd Shield master is clearly better off using TWF than twohanding his shield.
Sometimes you are stuck using TWF because of you class.. Monks.
THF just works out of the gate, letting you gain feats like Cleave or Whirlwind attack. THF gives you reach options which is great. Compared to THF, TWF is weak. But you can make it work if you take a class with support for it and invest the feats.
from an optimization standpoint, TWF is only really worthwhile when you have an exceptional static bonus to damage, or a significant source of extra damage that applies to every attack... a rogue/ninja can make great use of TWF (if they can get their attack bonus high enough) because when flanking they get to add sneak attack to every attack; paladins actually can also make great TWFers, a couple times a day- the extra attack bonus from smite makes up for the attack penalty and you get the bonus smite damage on every single attack. i haven't played one but a cavalier might be able to do a similar thing with challenge.
2 exceptions...
rangers: they can pump Str (since they don't need to meet Dex requirement for feats), and sometimes have favored enemy bonuses, so they can use TWF fairly effectively.
kukris: a dex based fighter TWFing with kukris can get up to an 'ok' amount of damage output, but more importantly they can take Butterfly's Sting- doubling their number of attacks nearly doubles their chance of earning a crit they can pass on to someone 2handing a x3 or x4 weapon!
Rather than repeat, I will echo the sentiments of Monkerdoodle, Thalin, and Imbicatus.
My peers have pointed out the obvious in TWF vs THF. However, you would go TWF for certain builds. For example, the extra attacks could let you set up more maneuvers during a full attack. There are some feats and classes that give you AC bonuses and other nifty tricks with two weapons. If you want big, consistent damage go THF. If you want to be tricky in your build or have a solid plan for getting in sneak attacks TWF may win the day. It just depends on the campaign, the group, etc. You know, like most 'this or that' questions.
As other have said, THF is simpler & more effective 90% of the time. ONe interesting exception is the "double sling", a ranged weapon that can be TWF'd for more shots that rapid shot+manyshot. However, it is a heavy feat investment.
Before 3rd edition, IIRC, you could dual-wield without penalties if you had a high enough dexterity score. That's something that Pathfinder needs to add, IMO. A feat with a 17 Dexterity requirement, BAB+1, TWF as a prereq, reduces the penalties to 0/0, even with two full sized weapons (2 longswords, for example).
The way things sit now, the only good TWFers in my experience are rogues and rangers.
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The way things sit now, the only good TWFers in my experience are rogues and rangers.
These guys beg to differ.
These guys beg to differ.
Saying that the only good TWFers are rangers and rogues does not also imply the inverse; that rangers and rogues are only good if they go TWF.
At lower levels, the difference isn't actually that great. Without Power Attack, I get about 7.15 DPR for an Earthbreaker/Great Sword vs. 7.0 for a long sword/short sword combo (6.1 if you don't have Double Slice). With Power Attack, it's about 7.9 vs. 7.3 (6.6 without Double Slice). It diverges more at higher levels, and as everyone pointed out, TWF requires a lot more work than a plain two-handed fighter.
You can make it work, though.
For fighters, weapon training accounts for a ton of damage, so you really want your weapons in the same group if possible. If you want to go TWF, consider picking up Exotic Weapon Proficiency in Sawtooth Sabres (1d8, treated as a long sword except you treat it as a light weapon in your off hand). It lets you apply all your weapon-specific feats (Weapon Focus, Weapon Specialization, etc.) to both weapons without being forced to use a light weapon, and both your weapons are in the same Weapon Training group. If you do Enlarge Person or Lead Blades, the damage dice goes up to 2d6.
Take Double Slice if your strength bonus is 4 or higher. Strongly consider it if your strength bonus is 2-3, but it doesn't have as much impact.
Power Attack is not as useful for TWF because of the off hand penalty. You take the full attack penalties on all attacks but only get half the bonus on your off hand attacks. It does give you a damage increase, but I'd have to progress across each level to see where the break points are (generally, if Power Attack/Deadly Aim drop your highest To Hit chance below 20%, you're better off without it).