@betsill
Brigantines accelerate faster than the other ships and slow down more slowly than them. They have a quicker rudder response time than galleons, but a wider turning circle. I mentioned anchor dropping because you mentioned it as something that was perhaps a disadvantage or similar, but on a sloop it is the easiest to recover from of any ship, whether you did it or another crew did.
Your goal with a sloop varies depending on your plans and strategies. Get close enough to a galleon and they can't hit you at all, and can't keg you without hitting themselves, too. If you can overpower them with strategy and skill in player combat, then you could win that way, getting them to pull away from the fight. Some players like to stay behind the ships they attack, sailing circles around the other ship to avoid cannons, harpoons and rams. There are many other strategies, too, far too many to put here. This also varies depending on whether there is one or two on the sloop.
I've won my fair share of battles against people with far more skill than me by outsmarting them where they relied on their direct power to get by. Regardless of how good they are, they still die from a blunderbuss shot, and their ship is still down a crew member or two - even with all of the skill in the world, two or three people on a galleon cannot deal with broken masts, a dropped anchor, hull damage, fire, other CCB effects, and firing back at the same time. Even if a sloop is shot at, it's still the slowest sinking ship, and can be bailed dry by two players with every hole open, and by one player with most of them open.
If I'm in a chase with a galleon (or brigantine, for that matter), I'm not going to make it easy for them. Shooting their crew from my ship, dropping kegs behind me (or Barrels O Plenty, I tend to keep one, it's a good trick), throwing firebombs, weaving in between islands and rock formations, all kinds of stuff. I've even won sloop chases by being more daring and risky with rock formations and the like - Shipwreck Bay, for instance, where I can weave through some rocks but many other ships do not follow. Or Thieves Haven, which a sloop can easily make it through without slowing. Another thing you can do is be more aggressive than they expect, do an anchor-turn to get a cannon facing them and open up with CCBs to stop them and then normal cannonballs to keep them busy. Some into the hull to distract them, then into their masts to keep them stuck for a bit - they'll leave those for last most of the time, and they take time to deal with at any point. Galleons also burn faster than any other ship (the rate of fire spreading scales up with the ship's intended crew size), so a firebomb or two on deck will keep them busy for a bit if they neglect it.
Essentially, a galleon can escape a sloop by simply sailing away. A sloop can escape a galleon by outsmarting and outplaying it. It's the same as every other situation: you can't win by direct force, they just have more, but you can win with strategy and awareness.