Pardon my ignorance, since I have little knowledge of the Western traditions of sword arts. I train in Filipino arts however, which were influenced by 16th -19th Century Spanish fencing as well as a blending of earlier Indonesian, Malaysian, Chinese and native traditions. At any rate I have a colleague at work who practices rapier fencing. He swords are long and his technique emphasizes thrusting, although there is some slashing and blade work. By contrast, most of the Filipino sword work I've seen uses shorter, broader blades, emphasizing cutting more than stabbing, although there is plenty of that too. I get the impression that the blades I've been exposed to may be more akin to a Western cutlass. That would make sense since the majority of Spaniards arriving in the Philippines would have been sailors,
This is a huge can-o-worms. There are basically two lines of thought on "western influence" in FMA. First, the FMA footwork, angles of attack, and movement patterns seem very similar to western, particularly (the thought goes) Spanish methods (destreza). However, the second theory goes, most of the contact would not have been with Rapier but with shorter, broader, cut-and-thrust blades used mostly by non-Spanish mercenaries (Portugese maybe? - I don't recall).
I should mention that there is a third theory that suggests simply a parallel evolution instead of a borrowing of ideas. The idea goes that the similaries are merely the result of the fact that the best way to swing a sword of a particular shape is pretty much the same whether the fighting style developed on the Filipines or in Europe.
and I've heard that the cutlass was used aboard ships for close-quarters fighting.
Over the years, all maner of swords have been used as Sea Swords. Straight, Curved, Double Ediged, Single Edged, etc. The primary trait being that they were (usually) fairly short to enable better use in the close quarters of shipboard combat. Try rapier fighting in a 6' cube sometime to see what I mean. The Historic Maritime Combat Association has some really good information on this.
http://www.historicalmaritimecombat.com/
I don't know what sidearms were used by soldiers of that period, or how these various different weapons would fare in combat against each other?
Depends. Tomahawks were even used shipboard, daggers, long knives, clubs, etc. Generally, they'd prefer to just shoot you, though.
Generally, I've always felt that the longer weapon has an advantage if there is room to use it, but then again I've seen the Wing Tsun Bart Cham Dao or short "Butterfly Swords" defeat a nine-foot "long pole", so clearly other factors come into play. Any input would be appreciated!
Depends on a lot of factors, of course. But, yeah. Longer weapons generally give you an advangate. There's a reason Pole-Axes were popular. Then there's Richard Peeke, armed only with a Quarterstaff, taking on three Spanish Rapier masters and winning his freedom.
The problem with long weapons is that, while they give you great advantage of reach, if the opponent can "pass the point" and "get inside" the weapon, then he has negated the primary advantage of your weapon. There's still options, of course (such as the butt-stroke/contrario, pummeling, and corps-a-corps fighting) but he's made it inside your guard and that's a bad thing for you.
Peace favor your sword,
Kirk