I like the look of the BSB on all accounts. In fact, I think the yellow lines are what makes it a standout, fun looking ship. Given the choice of one and only one, I would take the BSB.
However, as far as battle on the open seas between the BBB and BSB, I think the BBB would win due to the raised, swiveling rear cannon. All it needs to do to gain the upper hand is run away from the BSB and shoot it while being chased. If you took these two ships, scaled them equally to full size, and had them going at each other it would only take a couple hits with their proportionally enormous cannons to severely cripple either craft. Given that the cannons are equivalent in nature, they would have the same default range/power. The range on the BBB's swiveling turret would be greater than the broadsides of the BSB due to its height and would not require repositioning of the ship to make use of the cannon should the BSB prove to be a faster craft and able to make it alongside. By the time the BSB got into position to deal damage to the BBB, it would be splinted and its cannons likely disabled or its crew dead. Unfortunately for the BSB, having two extra cannons and 4 extra crew would only mean that two cannons will go unused and more people will die. Even if the two ships began next to each other and merely traded broadsides, the BBB would win because it has three cannon to the BSB's two and the third cannon is in an excellent position to rain destruction on the BSB's cannon crews, masts, and everything else on the deck.
Outside the captain of the BBB being incompetent, the BSB's only possible winning scenario would be if it were a defending craft in a relatively small, narrow-mouthed cove into which the BBB would necessarily have to sail in order to get line of sight on the BSB. At which point, the BSB could fire into the BBB with a broadside while the BBB itself could not return fire. The BSB crew may even find a way to move the other two cannon to the same side and use 4 cannon against the BBB in that situation to win faster, but from the layout, that would take some time. Having the extra personnel will help.
+1 for BSB to own
+1 for BBB to win