Diablo – Comparing a two-hand weapon with two one-hand weapons in the inventory

When you dual wield, you alternate attacks with your weapons. So the damage of your skills will change between each strike. That's why when you equip a significantly lower damage weapon in your offhand, your net damage could possibly go down.

Source

You're looking at DPS, not Damage, right?

Two Handers tend to be slower - you attack much less frequently - but hit much harder. This is particularly useful in combination with the way several channelled or high-cost skills work - you'll conserve your resources more while doing comparable damage with a big heavy weapon, at the cost of defense, or possibly some extra damage. You'll also want to take a look at this question for a rundown on dual wield mechanics:

How is listed DPS calculated when dual-wielding weapons?

(Your class also comes in to play here. For example, Demon Hunters using a 2h such as a Bow instead of a Hand Crossbow can still equip a Quiver in the OH, retaining the stat bonuses from the offhand slot).