Finesse weapons allow you to use Dex for attack and damage rolls. This allows most of classes, including even some first-line fighters, to dump Str for Dex – you do not lose in attack rolls, only a little bit in damage rolls (there are no finesse two-handed weapons, but a rapier with d8 dmg is still pretty good), you gain a lot in AC, and as a bonus you have excellent ranged attacks. You cannot really grapple etc., but you easily avoid such attacks.
Having low Str incurs some limitations like lower carrying capacity, but this seems to be more than offset by having good Dex skill checks. All in all, having a power-focused fighter against a fighter with this kind of optimization, my bets would be strongly on the second one. Am I missing something?
(Of course, the DM can have something to say on that, and it may also look like poor role-playing; but let’s put aside those for now.)