Trying it out in game can be rather difficult considering the general lack of the necessary characters/builds, or lack of a test area/server, so unless I work my butt off leveling a barbarian or someone with it speaks up it isn't happening too soon
So, paper theorycraft:
Example build: Barbarian 15/Fighter 12/Rogue 3, starting 18 STR/CON(with gifts), CON focused, with terrifying rage.
The barbarian
738 HP;
28 AC(no natural armor/DEX pot/shield);
34 AC(no natural armor/DEX pot);
38 AC(natural armor, DEX pot and shield);
73 HP(max CON);
42 AB(max STR);
Saves: Fort 31/Will 11/Reflex 11(max CON, no save items);
(Base weapon damage)+16+4 essence(max STR, no criticals included);
(Two handed weapon damage)+21+essence(max STR, no criticals included);
Rage: Will boosted to 30, damage return of 15, vampiric regen of 5, 50% movement speed;
DR: 11/-.
Alternatively, you could go for CoT instead of fighter, exchanging damage for saves, but won't be getting any of the CHA bonuses without some crazy stat spreading or sacrificing STR/CON. If you know of a better barbarian build feel free to speak up.
Staple 20 ftr 7 WM 3 rogue gets the following average:
45 AC(without natural armor or expertise);
48 AC(barkskin potion, no expertise);
48 AB(max STR);
558 HP(max CON);
Saves: Fort 24/Reflex 13/Will 9(no save items, max CON);
(Base Weapon Damage)+24 physical+4 essence(max STR, no criticals included).
I don't know how to properly build a paladin/BG, but it goes something like 20 Fighter/3 Rogue/7 Paladin(or BG), it gets more AC and saves than a WM, okay smiting, a bit less AB, and less physical damage/critical damage. It can beat the staple ftr/rog/WM.
PvP Scenario:
Barbarian VS Staple Scimitar WM
AB vs AC
42 AB vs 48 AC(53/58 with expertise);
38 AC(32 no shield) vs 49 AB(44/39 with expertise);
Even with IMP expertise, the WM will hit a barbarian with an adamantine tower shield without failure, while the barbarian will have to roll 16 or higher to land a blow at his highest attack. Terrifying Rage will lower the WM's AB by 2, but even then it won't last too long unless the barbarian runs around like a goofball.
Survival
The barbarian won't be able to use his vampiric regen effectively because he has to land blows to begin with, his DR of 11 and 5/- essence will only be able to mitigate 15 damage out of an average of 31.5, still taking 16.5 average damage. The WM won't be hit too often to worry about his own survival, and can even outlast the barbarian's rage if the barbarian doesn't dies first.
Damage Output
Considering the WM will land majority of his blows, suffice to say a LOT of them will critical hit, and that will hurt so much. At 3x multiplier, the average damage of a scimitar will be 96.5, that's super threatening even for 608 HP. The barbarian will struggle to land blows and they won't be too damaging, so his main source of DPS will be from his biteback damage, which happens to be 15, just about the same of the average damage of a non-critical hit from the WM against the barbarian.
UMD
A barbarian can use true strike potions/wands to try and hit the WM,
however, that'll give the WM ample time to bash down the barbarian or just kite the barbarian till it wears off. Word of Faith, Flesh to Stone, etc. can be used by either with the same output.
Where a barbarian can succeed where a WM can't?
I don't know
PvE Scenario
Damage Output
The WM trumps over the barbarian in a landslide as far as melee damage goes. The only way for a barbarian to out damage a WM in PvE, is if they're completely surrounded by foes who are hitting the barbarian without doing enough damage to threaten him, and with how low the biteback damage scaling is, it will rarely make up for the it.
Survival
The barbarian should be able to reliably hit majority of mobs of his level to trigger vampiric regeneration, BUT, if the damage you're taking is greater than the HP you're making, it's probably a good idea to get more AC, which is a direct counter act to biteback damage. If they go for bite back damage and they go against more than one enemy, they might need someone to heal them frequently. A WM has tons more AC.
What the barbarian does better in PvE?
Not damaged by rippers.
pls dont hate me mith im just tryin2help