Well, assuming no multiclassing is a rather dangerous assumption. The most common multiclass I see around where I live is Barbarian/Fighter. (The traditional mix is Bbn 1 or Bbn 2/Ftr the rest of the way, but I know of one 14th level Ftr 6/Bbn 8). The first two levels of Barbarian give rage, fast movement, and Uncanny Dodge which is well worth two fighter levels. After that, it's 5th level before you get a new ability worth having (the 2nd rage at 4th level is nice but Extra Rage can substitute for it). OTOH, the first two levels of fighter give you a feat at each level and then 4th level fighter gives you weapon specialization.
But, multiclassing aside, why play a fighter instead of a barbarian?
1. Barbarians deal out a lot of damage, but they also take a lot of damage. A typical barbarian IME takes at least twice as much healing as a more defensively oriented character.
2. Fighters have a lot more defensive options. Tower shields and Combat Expertise are probably the two most commonly used ones. However, Improved Trip is a great feat for fighters and, while barbarians could take it, most single-classed ones don't because they don't get many feats and taking a feat that doesn't work with Rage (Combat Expertise) isn't a good deal. Furthermore, a lot of them dump int and couldn't get it if they wanted it.
3. Fighters do non-two handed weapon fighting better than barbarians. A barbarian could use a sword and shield. But he usually doesn't want to. Rage gives more extra damage if he uses a two-handed weapon. Furthermore, rage diminishes the Bbn's AC which is the point of the shield to start with. Greater Weapon Specialization, OTOH, works just fine with a one-handed weapon.
4. Fighters are the best damage dealing archers out there, hands down. Even the complete books don't have prestige classes that an archer could take that give him something better than Greater Weapon Specialization. Barbarians, OTOH, don't make great archers because they would need to carry a non-raging bow and a raging bow to take advantage of their increased strength without spending all their non-raging combats at -2 to hit. Furthermore, weapon focus and greater weapon focus help archers attack rolls. Rage doesn't.
5. Fighters do two weapon fighting better than barbarians. If you take a two bladed sword fighter or an oversized two weapon fighting fighter with two waraxes or bastard swords or mauls or whatever, and apply rage, he gets +2 atk and +2 dmg with his primary hand but only +2 atk, +1 dmg with the other. A fighter, OTOH, gets +1 atk and +2 dmg with both blades--+2 atk and +4 dmg with greater weapon specialization. (And Greater Weapon Spec. is much better than greater rage for this).
6. As for feats, 8 feats is not enough to truly master a style of combat. (And even if it were, mastering a style of combat at 18th level doesn't let you enjoy it for as many levels as mastering a style at 8th level does). For instance, consider the following chains:
Archery: Point Blank Shot, Precise Shot, Rapid Shot, Manyshot, Improved Rapid Shot, Improved Precise Shot, Weapon Focus, Improved Crit, Weapon Specialization, Greater Weapon Focus, Greater Weapon Specialization, Quickdraw (12 feats--9 if you don't count exclusive fighter feats).
Two Handed Weapon Damage: Power Attack, Improved Sunder, Combat Brute, Improved Bull Rush, Shock Trooper, Leap Attack, Dodge, Mobility, Elusive Target, Improved Critical, (all 4 weapon focus/spec feats)--14 feats--11 if you don't count fighter exclusive feats. A fighter who has all this can charge, leap attack, power attack for his full BAB, apply the entire penalty to his AC instead of his attack (meaning he'll still almoster certainly hit), sunder his opponent's weapon, cleave through into the opponent, and then put his dodge on whoever looks the most dangerous and avoid all of the extra power attack damage that he'd usually take for dropping his AC with shock trooper (because of Elusive Target).
Two Weapon Fighting: TWF, Imp TWF, GTWF, Oversided TWF (or EWP: Double Weapon), Power Attack (for when you make a single attack or normally if using oversized TWF), Imp Crit, Weapon Focus, Weapon Specialization, Greater Weapon Focus, Greater Weapon Specialization, (10 feats--7 if you don't count fighter exclusive feats)--you could also add Two Weapon Defense and Imp Two Weapon Defense or Imp Shield Bash to the list, but I think an animated shield is a better buy than those feats.
So, while you could eventually master one of these styles as a barbarian, it would take you until 18th level and even then, your trick would be that you had mastered that style--you wouldn't have any of the other options--Close Quarters Fighting, Cleave, Great Cleave, Combat Reflexes, Improved Trip, Combat Expertise, Improved Disarm, etc. that a fighter will have. A fighter can master a combat style before 10th level and STILL learn a bunch of tricks that give him options beyond attack, power attack, and do damage.
