Barb in PoE is kinda similar to rogue in a way - vulnerable melee DPS. The main difference is that the dmg is spread among few mobs, instead of concentrated on one.
This makes him less viable on PotD, at least at the beginning, where it's better to shred something fast and move to the next one, instead of chipping everyone slowly. Later on he's catching up - mailny due to 2H on-crit weapons.
Yeah, but that's not really true. Unless you build and equip him to be a glass cannon that is.
Rogue is low defense, low endurance & low health.
Barb is medium defence, highest endurance & highest health. And it's quite viable to use heavy armor and have moderately high defence, particularly while dual wielding, which can reach 0 Recovery anyway. There are even pretty good shield Barbarian builds (and OP retaliation Barb builds, although they have been nerfed, as I understand) .
Highest Health all the classes, combined with possibly high Strenght for healing effect boost, makes Endurance regeneration effects exceptionally potent on Barbarians. They have the Savage Defiance Talent. Coupled with other sources, like possibly Shod-In-Faith and Moon Godlike Silver Tide make the Barb almost unkillable - as long as his Health pool lasts. Good news is that his Health pool is the greatest of all the classes and with some Con it can become truly monstrous. I think he's actually a very good candidate for the Wound Binding Talent, to keep him rocking even longer between the rests. With high might and some health boosting talents he can restore over 1000 health in 1 use, I think.
So they do take damage (unless built to be tanky, which is viable), but can recover it rapidly as well. And dish out even more.
Only enemies they are kinda weak against are the major bosses with huge Deflection and Fortitude. They can be debuffed to be fought effectively by the Barb... but other classes do it better. Then again, most of them have minions... and the Barb really owns hordes of regular mobs. Even moreso if they have low Fortitude (or get Fort debuffed, which the Priest can easily do with Painful Interdiction). For example Llengrath went down so fast I couldn't believe it.