Guess:

The slower ship would never be in a position to get caught without making a mistake, but it’s turning advantage rapidly reduces with with distance, so it would never be able to get away in the long run.

Confounding factors: Ship lengths. As the ships get longer relatively their turning circle, the easier the slow ship becomes to catch. The length of the ship makes it harder to dodge.

Conditions of capture and escape. Are we talking about being side by side, close enough to through grappling hooks, or just a point touching? Or cannon range? Is escaping getting out of line of sight? RADAR range?

Islands. This favours the more manoeuvrable ship as the fast ship cannot take a straight line course. It also increases the fast ships cost for falling for bluffs.

Acceleration and speed cost to turn. Overall, introducing these makes the engagement longer. That said, it would also affect the fast ship more if islands are introduced.

Outside objectives. Ships can’t be at sea forever, and likely both ships have places to be. Is a vital shipment of vaccines on the slow ship? Does the fast ship know this? Etc