Not disagreeing completely, but it does heavily depend on the weather and often not to the advantage of the smaller ship (and I do think that the speed differential would in real cases be measured in fractional knots). In heavy seas - heck in typical North Atlantic conditions most of the year - a 19th century frigate is going to be in serious trouble if a major warship challenges it.
Not necessarily--in such heavy seas, the Ship of the Line is going to be unable to open her lower gun ports for fear of taking on too much water. Furthermore, both ships are going to be heaving or heeling so much that there is a real risk of being hulled below the waterline. Under the circumstances, neither captain is likely to want to pick a fight, because even a victory might leave them unable to make it back to port easily with damage they're unable to repair. Again, there's also the fact that frigates could sail closer to the wind, meaning that speed becomes much less relevant if she's trying to escape.
I don't dispute you that if a frigate did somehow end up in combat with a SotL, the results will likely not be to the frigate's advantage (with the possible exception of a US '44 engaging an old 4th rate under ideal circumstances). But the circumstances required for that to happen will be such that either the frigate captain will have (idiotically or recklessly) passed up many chances to escape, or the seas are heavy enough that both captains will be more concerned with preserving their own vessels than in engaging the enemy.
I will concede that I have overlooked the difference in rigging's - used to most boats being comparable in key technologies in real life. Out there, there is a reason why races are organized according to class and size. (Yeah, I used to drive boats, once upon a time.)
As someone else who sails, I get where you're coming from. But yeah, the situations involve with three-masted square-riggers are much different from modern racing boats.