Okay
Whilst TCOB is very likely inspired by some version of TSOD they have little text in common as one might expect with almost a couple of centuries between them. The lines of narrative they have in common are what we would call commonplace to these maritime skirmish encounters, though I would hazard a guess in this case there is a direct descent. The most obvious connection is the second refrain 'along the coast of Barbary'.

TSOD is a ballad of 2 encounters between a French Man-o-war and 2 English merchant vessels. The Sweepstake is captured by the Frenchmen and The George Aloe then sinks the Frenchmen.

TCOB again we have 2 English ships King of Prussia and Prince of Wales and they have a battle with a pirate ship and sink it.

There are similarities here with the numerous adaptations of Phil Saumarez's encounter between the Nottingham and Mars of 1746; at least
half a dozen versions give different encounters between different sets of ships right into the mid 19th century, using basically the same wording.