There are several "mathematics" way to compare the different styles. Here is mine:
I compute it another way then usual, I do not take into account multiple hits but think more about the probability of just one hit and the average damage due to this hit.
Let`s assume two 4th level Fighters.
They will be equal in everything expect two feats.
We will use only situations where you can use full attacks. (This is one of the greatest problems with all this comparing)
Fighter 1 chooses: Ambidexterity, Two Weapon Fighting
Weapons: Longsword, Shortsword.
Fighter 2 chooses: Weapon Focus (Longsword), Weapon Specialisation (Longsword)
no further differences.
We will ignore Strength bonus - at least for now. And we will ingore the greater probability of a critical hit when wielding two weapons - this might or might not be compensating each other.
Fighter 1 gets 2 attacks at his highes base attack (with a penalty of -2) This means he can roll 2 x D20. Allowing two rolls of a D20 is approximately equivalent to rolling 1d20 with a +10 bonus.
If we only "want" him to hit once, he as a +10 bonus, with an average damage of (average of a 1d8 + average of a 1d6)/2 = (4.5 + 3.5)/2 = 4.
His effective attack bonus is +8, not +10, since he loses 2 points due to fighting with two weapon (we still have to take this into account)
Fighter 2 uses his standard base attack without special penalties.
His average damage is 6.5 points with a +1 to attack.
To make math a bit easier, the +1 attack bonus can be converted to damage due to power attack, so average damage 7.5 with +0 to attack.
(Both Fighter should have been able to get power attack)
To make Fighter1 "damagewise" equal to Fighter 2, he could use power attack. Rounding Fighter 2´s damage up to 8, to make math easier. Power Attack +4 makes both fighters equal in damage, reducing Fighter 1s attack bonus from +8 to +4.
Regarding AC: A Large Shield grants Fighter 2 no penalties in battle. It gives him at least a +2 bonus to Armor Class, it might even be greater considering magic enhanced shields.
Expertise can be used to get Armor Class up for Fighter 1 (A Fighter level 4 has 3 bonus feats and 2 standard feats, so he could still afford this)
Thus, Fighter1 is better when the total AC Bonus from Fighter2`s shield is not greater than +3, equal to him when its bonus is +4, and worse when his bonus is greater than +4.
(His net advantage would be +4 - (Fighter2 Shield`s AC Bonus) )
Now we get a 3rd fighter (let`s call him Fighter 3), he wields a Greatsword (average damage 7 without special bonuses).
His "free" 2 feats are, obvious, weapon focus (Great Sword), Weapon Specialisation (Great Sword), giving him a +1 to attack and a +2 to damage, using power attack to reduce attack bonus to +0 he inflicts a total damge of 10 points.
Let us assume that you could subtract points from damage to raise your AC (this makes math much easier), he could add a total of +2 to his AC and subtratcing 2 from its Damage to be equal to fighter 2 using a Large Shield without bonuses.
(If we take into account that fighter3 get`s more strength bonus, he would be better than fighter2.)
To get fighter 1 to be as good in damage dealing as fighter3, he would have to bump up his average damage from 4 to 10. Using Power Attack (ingoring the maximum possiblity for it) he could add +6 to damage and reduce attack bonus by 6 to a total of 2.
In this case, fighter one has a 2 points advantage to fighter 3, which is equal to his advantage to fighter2 with a nonmagical large shield.
Still missing in this calculations:
a) Full consideration of strength bonus to damage
b) Any situation in which only one attack is allowed and extra attack from high Base Attack Bonus (whithout Improved Two Weapon Fighting: Advantage Fighter 2 & 3 and when moving and attacking: Figher 2 & 3).
c) Costs for weapons.
d) Special Feats especially from "non"core Books (Shield Expert can completely change balance when you use shields as offhand weapon, especially when using Shield Spikes, but there might still be other feats for one handed and two handed fighting styles; Twin Sword Style from Forgotten Realms)
e) Using Special Weapons, Weapon with Reachs, Double Weapon (especially considering Weapon Focus/Specialisation).
(Fighter 2get`s slightly better when using a Bastard Sword, but the same applies when Fighter 1 switches to Orc Double Axe or Double Sword)
f) Linked with the costs for weapons: Pentrating Damage Reduction (Fighter2 and Figher3 are more likely to get better enhancements for their single weapon)
g) Versatility (Switching Weapons especially with Weapon Focus/Specialisation; Fighters switching styles especially at high levels.)
h) Ability Requirements for feats (Fighter 2 & 3 will most likely not have a high Dexterity)
i) Differend classes: Rangers cannot use Double Weapons with ease. Barbarians cannot wear Heavy Armor and are more likely to get a high Dexterity, more easier qualifying for Ambidexterity, but lack some feats (can`t get Weapon Specialisation unless multiclassing) and so on...
So, all in one:
I believe, all styles are relatively equal, and it is really a question of what you prefer. There is no real "better" in here.