Because the feat combat expertise gives only a bonus of +1 in AC, when the feat Power attack gives a +2 bonus in damage? When both ask for the same penalty.
why not the same bonus?
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Don't ever take Combat Expertise unless you really really want it. Take Dirty Fighting instead. It qualifies you for everything Combat Expertise does (and more), and it's legitimately useful because if you're ever flanking someone you can do any Combat Maneuver you want without provoking AO's.
Dirty Fighting (Combat)
You can take advantage of a distracted foe.
Benefit(s): When you attempt a combat maneuver check against a foe you are flanking, you can forgo the +2 bonus on your attack roll for flanking to instead have the combat maneuver not provoke an attack of opportunity. If you have a feat or ability that allows you to attempt the combat maneuver without provoking an attack of opportunity, you can instead increase the bonus on your attack roll for flanking to +4 for the combat maneuver check.
Special: This feat counts as having Dex 13, Int 13, Combat Expertise, and Improved Unarmed Strike for the purposes of meeting the prerequisites of the various improved combat maneuver feats, as well as feats that require those improved combat maneuver feats as prerequisites.
Unless you want to be a student of war or a devoted muse. Those still require Combat Expertise.
Because martial's can't have nice things.
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Don't ever take Combat Expertise unless you really really want it. Take Dirty Fighting instead. It qualifies you for everything Combat Expertise does (and more), and it's legitimately useful because if you're ever flanking someone you can do any Combat Maneuver you want without provoking AO's.
Dirty Fighting (Combat)
You can take advantage of a distracted foe.
Benefit(s): When you attempt a combat maneuver check against a foe you are flanking, you can forgo the +2 bonus on your attack roll for flanking to instead have the combat maneuver not provoke an attack of opportunity. If you have a feat or ability that allows you to attempt the combat maneuver without provoking an attack of opportunity, you can instead increase the bonus on your attack roll for flanking to +4 for the combat maneuver check.
Special: This feat counts as having Dex 13, Int 13, Combat Expertise, and Improved Unarmed Strike for the purposes of meeting the prerequisites of the various improved combat maneuver feats, as well as feats that require those improved combat maneuver feats as prerequisites.
No it doesn't. There are many useful feats that still need Combat Expertise since they do not count as "improved combat maneuver feats". Example: Pack Flanking.
Weapon Focus* gives you +1 to hit.
Dodge* gives you +1 to AC.
If we assume that +1 to Hit is equal to +1 to AC, then Combat Expertise isn't worth the feat because your net gain is zero.
The same could be said about Power Attack, but that one is needed to actually deal damage.
*Not that I ever take these feats unless I'm forced to.
Power Attack is worth it because for most characters, +1 attack < +2 damage. For instance, for a lvl10 fighter with 22 strength, wielding a +2 greasword, attacking an average CR10 monster (AC24), +1 to attack rolls increases the average damage by the same amount +1.4 to damage rolls would. That's before you get into regions where your full BAB attcks are hit-capped, i.e. only miss on a natural 1 already. FYI, for this sample character, Power Attack increases the average damage by the same amount 3 bonus damage would.
High damage bonuses (e.g. Swashbuckler's Precice Strike), or moderate damage bonuses coupled with low accuracy, can shift that, as does the effective 1:1.5 ratio from TWF, but for non-extreme cases, +1 attack < +2 damage.
Using the official monster creation guidelines as a base, for a fight with infinite health on both sides (to remove thresholds), our Fighter has 25 AC (full plate, I'm using ABP), we can theoretically compare AC and attack:
For our sample fighter, +1 AC is worth +1.12 attack, which means that Combat Expertise is actually profitable, but just barely so. Dodge would be a better feat than Weapon Focus, but both are ~7 (WF) or ~8 (Dodge) times better than CE. Combat Expertise would nee a 1:1.23 ratio to be on par with Dodge.
Note: In practise, +1 attack is generally better than +1 AC because it also helps against enemies that don't just attack your AC.
Nothing breaks the game faster than a character with a really high AC/Touch AC.
Plus high saves, plus high CMD, plus flight, plus the ability to actually hinder the enemy. Unless every combat is in narrow spaces on the ground against enemies that don't use anything but regular attacks... in which case just about everything can "break the game".
Suppose then. A warrior with a lot of skill and little strength.
STR 12 Feats: Dodge, mobility, combat expertise, spring attack,
DEX 18 whirlwind attack
This warrior faces one that is the opposite.
STR 18 Feats: Power attack, Cleave, great cleave, improved sunder,
DEX 12 Improved bull rush
Both are of the same level (10th), with feats, ONLY OF CORE RULE BOOK, related to their stats: Who do you think has more chance to win?
Suppose then. A warrior with a lot of skill and little strength.
STR 12 Feats: Dodge, mobility, combat expertise, spring attack,
DEX 18 whirlwind attack
This warrior faces one that is the opposite.
STR 18 Feats: Power attack, Cleave, great cleave, improved sunder,
DEX 12 Improved bull rushBoth are of the same level (10th), with feats, ONLY OF CORE RULE BOOK, related to their stats: Who do you think has more chance to win?
Dex Warrior, Dexterity is the king of pathfinder. Even with those ridiculously suboptimal feats, dex is gonna hit way more often, likely go first in init, and take less hits.
If we only look at attacks, removing all feats but Dodge, CE, and PA, and using ABP (plus pips, so we're talking about a main stat of 22); both are wielding greatswords, as above, Weapon Training and Armor Training are included:
The Dex Fighter does an average of 7.3 DPR (against AC25), the Str Fighter 16.5 (against AC 31). The later isn't using PA, though, or his damage drops to 14.4 (or 19.1 with Furious Focus added, so that both are using two feats).
If we only look at attacks, removing all feats but Dodge, CE, and PA, and using ABP (plus pips, so we're talking about a main stat of 22); both are wielding greatswords, as above, Weapon Training and Armor Training are included:
The Dex Fighter does an average of 7.3 DPR (against AC25), the Str Fighter 16.5 (against AC 31). The later isn't using PA, though, or his damage drops to 14.4 (or 19.1 with Furious Focus added, so that both are using two feats).
A DEX fighter is not going to want a greatsword, he's going to get rid of the mobility, spring attack and whirlwind and go for weapon finesse, twf and (in favor of high AC theme) two weapon defense.
I know, but I was using the given example.
Ok, let's pit a dex build with TWF, iTWF, WF and TWDef (AC28) using two shortswords agains a strength build with, no feats: 15.8 vs. 19.6 DPR.
I did also make the hypothetical fight with a dex build with Dodge, CE, Weapon Finesse, Fencing Grace, and a Rapier. DPR was 16.3 iirc.