Think about it before you ask questions like this. When I say they should be "roughly equivalent in terms of damage" that means that there may/should be circumstances where one build would outperform the other but on the balance they contribute roughly the same damage per encounter. In other words, both builds should be viable and neither one should too often outclass the other. That's not the point though. The point is attribute scores, if too tightly integrated into combat, make this kind of balance that much harder to achieve.
Ok, it may seem like my question was stupid. What I was trying to ask is: if you don't add Str to damage (or do add Dex for finesse fighters), how do you differentiate them?
In 3e, TWF means you need higher Dex -> lower Str -> lower damage/hit, but more attacks. For one weapon finesse classes (duelist, swashbuckler, etc.) there is precision damage instead, which is somehow conditional.