Not sure about which specifics to get into, but brigantines were considered unweatherly and top-heavy, and generally undesireable to take out into deep sea. They tended to easy pitch over and sink in storms. They were second only to frigates for coastal warfare and escorts, though.

Merchantmen, or East Indiaman, were "heavily" armed trading vessels. They often looked like ships-of-the-line, and indeed, tried their best to look like one. They would pierce additional gun ports to give the appearance of a fierce warship, and often had a large number of guns. They never stood up against a proper warship however; the crew of such ships were generally ill trained, and the guns aboard were pretty much 6-pounder popguns. It was a [url=http://en.wikipedia.org/wiki/Action_of_4_August_1800]pretty big deal[/url] if an East Indiaman did anything besides surrender. 

Not too familiar with Spanish galleons and the like, but vessels such as the sloop, barque, and the brigantine were pirate favorites.