The penalty from Combat Expertise applies to all attacks for 1 round starting when the standard attack action or full attack action is taken
Because the benefit of the feat Combat Expertise (Player's Handbook 92) applies when the standard attack or full attack action is taken—not, in the latter case, when each iterative attack during the full attack is made—, the feat's benefit can typically apply only once per round. (For more on the feat's language, see this question.)
A fighter 6 takes a standard action to make a standard attack and uses the feat Combat Expertise to penalize his attack rolls by −2. He gains until the start of his next turn a +2 dodge bonus to AC, and he suffers a −2 penalty on that standard attack's attack rolls and a −2 penalty on any other attack rolls he makes until the start of his next turn (these other attacks are usually attacks of opportunity).
A fighter 6 takes a full-round action to make a full attack and uses the feat Combat Expertise to penalize his attack rolls by −5. He gains until the start of his next turn a +5 dodge bonus to AC and he suffers a −5 penalty on each attack roll he makes during that full attack and a −5 penalty on any other attack rolls he makes until the start of his next turn (such attacks are usually attacks of opportunity).
To be clear, the fighter can't, for example, take the full attack action, employ the feat Combat Expertise to suffer a −1 penalty on his first attack roll to gain for 1 round a +1 dodge bonus to AC then on his second attack roll opt to suffer a −4 penalty to gain for 1 round a +4 dodge bonus to AC. The entire penalty is assessed (and the entire corresponding bonus gained) when the fighter initially opts to gain the benefit of the feat Combat Expertise—when the fighter takes the standard attack or full attack. The penalty can't be meted out separately so as to spread it out among the fighter's attacks. (That would be awesome, though, were the fighter able to make a full attack and be able to suffer the penalty for the feat Combat Expertise on his last attack—an attack that probably wasn't going to hit anyway—and gain for 1 round the dodge bonus from the feat! But that's not how the feat works.)
Combat Expertise versus Power Attack
The feat Combat Expertise does, indeed, pale in comparison to the feat Power Attack (PH 98), but that's not because of when, how often, and to what degree the feats' users can apply the feats' benefits but because the feat Power Attack is almost always used, and the feat Combat Expertise is used sparingly.
The feat Power Attack is often used on every attack because more damage means a quicker end to a threat, and dead foes stop trying to make the attacker dead. However, the Combat Expertise feat's benefit is typically dependent on the circumstances: when this longtime DM's seen it used, the user's been in situations that are either desperate or already in the user's favor. In short, typically, the feat Power Attack is for when you're winning, and the feat Combat Expertise is for when you're losing, and, because of the way the game's structured, most of the time, PCs will be winning.
That's not to say the feat Combat Expertise is always bad. The feat is, as this fine answer mentions, a sometimes-prerequisite for the feat Improved Trip (PH 96), a cornerstone of one of only 2–4 mundane combat styles that can serve a PC well throughout his adventuring career. Further, as a DM, I've had smart, cash-poor high-Hit Dice monsters take the feat Combat Expertise and use it consistently—every round—because that +5 dodge bonus to AC is often significant against equally challenging foes. However, to give you an idea of its rarity among PCs, in the past three campaigns that I ran that went from character level 1 to the mid- to high teens, of the 20 or so PCs who saw regular play none had the feat Combat Expertise, and that includes those PCs whose primary lifestyle choice was toppling foes and beating them when they tried to stand.
Thus, generally, this DM and player recommends that if there's a way to avoid having a character take the feat Combat Expertise—like by getting the feat Improved Trip from the wolf totem barbarian variant (Unearthed Arcana 49) or as a monk bonus feat not at level 6 but, by mixing and matching fighting styles, at level 2 (UA 52)—then the character should avoid taking the feat Combat Expertise.
Forcing Combat Expertise to have some value
When a warrior specializes in the feat Combat Expertise, the feat is capable of providing an unmatched degree of mundane defense. For example, by also taking the feats Allied Defense (Shining South 19), either Superior Expertise (Deities & Demigods 51) or Improved Combat Expertise (Complete Warrior 100), and by spending at level 1 6 skill points to acquire the special ability Bishamon's Blessing (the Wizards of the Coast-licensed Fortunes and Winds 77), a level 10 character with a full base attack bonus can opt to suffer for 1 round a −10 penalty on his attack rolls to grant for 1 round himself and allies adjacent to him a +15 dodge bonus to AC.
To be fair, though, the feats Allied Defense and Superior Expertise aren't fighter bonus feats so they must be taken upon leveling up, and such feats are extremely valuable to a fighter. Further, I suspect that over 90% of readers haven't heard of Fortunes and Winds, much less Bishamon's Blessing. Also—and probably a greater concern—, is that it's unlikely the character will hit with his attacks without further resources devoted to this tactic, like the arcane duelist (Random Encounters Web column "Way of the Sword") prestige class's extraordinary ability dexterous attack or one of the feats listed in this question, the ability to cast a spell like the 2nd-level Sor/Wiz spell wraithstrike [trans] (Spell Compendium 243), or a magic item or magic weapon that has an effect like the heartseeking amulet (Magic Item Compendium 110) (3,000 gp; 0 lbs.). (Note also how magic is still largely necessary to make this character at all effective!)
Even if he never deals damage and probably isn't that much fun to actually play, a character who can grant adjacent allies a +15 dodge bonus to AC will be, at least among his allies, popular.