Since we are breaking this down from a power gamers perspective, lets do it.
Proposal from OP: Ambidexterity, TWF for penalty-less TWF.
2 feats used. During full attack action, 1 extra attack at max bonus.
Lets assume a str of 14 and a dex of 14.
The other side of the fence.
Two Hand Power Strike, Weapon Focus: Greatsword.
Strength of 17.
Assuming level 1:
TWF: +3/+3 Hits with dual shortswords(less feats) for 1d6+2, and 1d6+1. Assuming an average ac of 14 for dex +1 leather armor having enemies, he will hit roughly %50 of the time, for an avg of 4.5 dmg/rd.
THF: +5. 2d6 +6. Same enemy as above, focused in greatsword, and has one. He will hit roughly %55 of the time, for 13/hit, for an avg of 6.5 per round.(roughly)
When TWF gets another feat, for ITWF, TWD, or others, THF gets Power attack, Cleave, Great Cleave, Improved Critical, Weapon Specialization, etc.
The fact is, TWF is only good if you have sneak attack, or weapons with massive bonus dice. If you are straight up fighting, you need a massive sword or axe and all your feats focused on beatdown, not on getting one more weak attack. That said, I prefer TWF without ambidexterity, as it means it costs you less feats to get. Feats are valuable.