The barbarian class in UA really is grossly overpowered compared to all the other classes (except, possibly, the cavalier). To refresh everybody's memory, here's their abilities:
*Double AC bonus for high Dex when wearing non-bulky armor (or no armor)
*Double hp bonus for high Con
*12-sided hit dice up to 8th level and 4 hp/level thereafter
*Base move 15"
*6 weapons of proficiency at 1st level (and 1 every 2 levels thereafter)
*-1 non-proficiency penalty
*Receive XP for destroying magic items as if item were kept
*At 4th+ level can hit creatures only struck by magical weapons
*+4 on saving throws vs. poison
*+3 on saving throws vs. paralyzation, death magic, petrification & polymorph
*+2 on saving throws vs. wands, staves, rods & breath weapon
*+1 on saving throws vs. spells per 4 levels (starting at 4th)
*Climb cliffs and trees (and walls, once they've had an opportunity to practice) as thief of same level
*Hide in familiar natural surroundings as a thief 3 levels higher hides in shadows
*Hide in unfamiliar natural surroundings as a thief of same level hides in shadows
*Surprise 3 in 6 (4 in 6 in familiar terrain)
*Only surprised 10% (5% in familiar terrain)
*5% chance/level to detect back attacks (negates attacker's bonus and allows barbarian free return attack even if he's already used his full actions for the round)
*Leap up to 10' forward, 3' backward, or 3' up from standing; 16-21' feet forward or 4.5-6' up from running; spring upward 4-7'
*Detect illusion: 5%/level (up to max. 75%)
*Detect magic: 25% at 1st level + 5% per additional level (up to max. 90%)
*Add level to charisma to determine effective charisma score when dealing with other barbarians
*Can perform "first aid" on self and others to immediately regain 1 hp and heal at twice normal rate (2 hp/day resting, 1 hp/day adventuring) thereafter
*10%/level chance to cure natural poison and disease (50%+victim's Con if poison or disease is known)
*plant and animal identification as 3rd level druid
*Predict weather as per druid spell (3rd level casting ability)
*Tracking as ranger of same level (outdoors only)
*Summon Barbarian Horde at 8th+ level (XP/1000 members + leader-types, will serve for [level] weeks)
And their drawbacks/restrictions:
*Must be human
*Cannot dual-class
*Min Str 15, Dex 14, Con 15 (though note that Method V char-gen allows the character the minimum required stats for the class if he fails to roll them)
*Max Wis 16
*No XP bonus for high stats
*Must have non-lawful alignment
*Does not automatically know alignment language
*Illiterate at start of play
*Initial weapon proficiencies must include knife, hand axe, spear
*Steepest XP chart of any single-classed character in the game (6000 XP for 2nd level) -- barbarians will tend to be 2 levels below thieves and 1 level below other classes with the same XP total
*First aid, plant & animal idenfication, predict weather & tracking abilities can only be used in familiar terrain (1 month of exposure required to familiarize)
*Must come from "some out-of-the-way barbaric state or area within the campaign"
*Cannot associate with clerics until 2nd level
*Cannot use potions until 3rd level
*Cannot use magic weapons until 4th level
*Cannot use magic armor until 5th level
*Cannot associate with magic-users until 6th level
*Cannot use weapon-like miscellaneous magic items until 7th level
*Cannot use protection scrolls until 9th level
*Cannot use other magic items available to fighters (rings, wands/staves/rods, non weapon-like misc. magic) until 10th level
IMO they're totally unsuited to standard group-based play -- they totally overshadow fighters and rangers, partially overshadow thieves and druids, and can't even be in the same party as a magic-user or illusionist until 6th level (which is 7th-8th level for everybody else). The barbarian is really only suited to a sub-campaign where it's the only PC (with perhaps one or two other fighrer or thief PCs or NPCs as "sidekicks") and in that case his overwhelming resilience and versatility make up for lack of numbers -- a barbarian and 1 or 2 other characters probably have about the same versatility and effectiveness as a full group of 6 "normal" PCs, at least at low levels.
We had a game like this back in the 80s -- one player with a barbarian PC, me as DM (and running a sidekick NPC/DMPC -- a halfling ftr/thief) -- and it was great fun as a change of pace from our concurrent standard/group-based campaign. We played through several adventures with just these 2 characters and the feel was much closer to the Conan, Fafhrd/Grey Mouser, and John Carter stories than any of our large-group play ever was. Plus, because there were only 2 of us involved, it didn't require a lot of advance planning and scheduling -- if we found ourselves with a couple free hours we could pull out these characters and play on the spur of the moment.
A sub-campaign like this can be a lot of fun, either as an adjunct to group-based play or for people who can't manage standard play (either from lack of free time or lack of other players), and the barbarian (as well as perhaps the monk) is the class best suited to it, because of their combination of toughness and versatility (combining features of the fighter, ranger, druid, thief, acrobat, and even a bit of m-u -- innate ability to detect magic and illusions). With a barbarian you can run modules that were intended for 6 players as-written wth 1-2 players and not have to worry about adjusting encounter strengths.