What team would win and why

A knight and a cowboy. Cowboys were often towards the later half of the period veterans of the civil war while a pirate was mostly a commoner who attacked vulnerable ships.

A knight vs an ancient warrior would not be as close a fight as you think as in addition to a 500lb horse a knight was often trained from the age of 5 in combat.

Just to be a total killjoy lol, Cowboys weren't the gunslingers who connected to the face with every punch like in the westerns. They were working so carrying a loaded sidearm would be ridiculous. A Warrior and Pirate were trained ruthless killers.

Back in the 00's there was a series on Spike TV that pitted such warriors against each other using computer simulations based on their strengths and common weapons and tactics, they even matched vampires against zombies.