The misconception
2-Handers are bad because they roll some sort of bugged 1-hander stats/affixes.
No.
The comparison
Here's an image comparing an old weapon with a new and improved Loot 2.0™ item: Immortal King's Boulder Breakers.
The one on the left has 1.6k DPS and dropped in patch 1.0.8. The one on the right has 1.1k DPS and dropped today, in patch 2.0.3.
Are the affixes bugged?
No.
If we take a look at the game guide for this item, we can see that the 2.0.3 version rolled correct affixes.
Guide says +(732–894)–(877–1111) Holy Damage, and this item rolled +770-986 Holy Damage. So the elemental damage is correct.
Guide says +495–787 Strength and this item rolled +580 Strength. So the strength roll is also correct.
Guide says 76–173 Life per Fury Spent and this item rolled 153. This roll is also correct.
Here's where things go wrong
The base DPS listed in the game guide for IK Boulder Breaker is 555 DPS
This means that the base item for this weapon should be a Titan Axe
If we remove the affixes from the 1.0.8 item we find out that the base item has 555 DPS. The 1.0.8 Boulder Breaker base item was an ilvl 63 Titan Axe.
But if we do the same thing with the 2.0.3 item, we find out that the base damage is 248.5 DPS. The 2.0.3 Boulder Breaker is not a Titan Axe. It's an ilvl 56 Battersmash.
Conclusion
In the transition from 1.0.8 to 2.0.3, The IK Boulder Breaker lost over 300 base DPS by having its base item changed from ilvl 63 to ilvl 56.
This is true for every single 2-hander in the game.
Skorn for example, is not an ilvl 63 Decapitator with 560 DPS as listed in the item guide, it's an ilvl 58 Valaska with 313 DPS
The most important thing: did this happen only to 2-handers?
No. 1-hander base items have been modified as well. It's just that the transition from ilvl 63 to lower ilvls has a way lower impact on the base DPS for 1-handed weapons.
For example, Azurewrath went from ilvl 63 Rune Sword to ilvl 59 Tulwar. By doing so, it lost 91 base DPS. Only 91, not 300+.
What is the developers' intention?
Their intention is definitely to make 2-handers the go-to weapons for certain builds. Their average damage is higher than 1-handers and this difference will be multiplied by affixes like % increased elemental damage and % increased skill damage.
With this model, 2-Handers will work with channeling skills, DoTs, high-cost or large-cooldown skills. But just at level 70.
small edit: Battersmash is ilvl 56 not 55
edit #2: ALL legendaries that had ilvl 61-63 bases have transitioned to ilvl 60 base or less: weapons, armors, off-hands. This is the reason why legendary mojos and orbs roll low damage.