These are all general, and everything is relative, and the differences are often really minor but...

Straight swords are better for thrusting. The whole blade is lined up behind the point, all on the same vector, and being lined up makes aiming easier. A straight blade can often have a narrower point, which is easier to get into gaps in armor as well. The double edge helps widen the wound or cut a bigger opening in padded armor. Some sabres have a point shaped for thrusting and the first few inches of the false edge sharpened, so they'd gain the advantages of this as well, but it's nearly universal on straight blades. A straight blade is a bit longer for the same weight, because of the whole "shortest distance between two points" thing. And if you have a straight, double edges sword, you can turn it around and use the other edge if one gets notched or blunted.

Curved swords slice better. If you just swing the weapon, the edge will naturally strike with a drawing motion. They are easier to keep aligned to hit with the edge as opposed to at an angle. There's a physics reason for this, and it was explained to me, but I don't remember it, being a grunt and not a scientist. Single edges blades can have a more acute edge for the same weight/ breadth of blade. A cutting edge is at the most basic concept, a wedge. Two wedges back to back will either be a lot broader than a single wedge, or much less acute. And you can get sneaky with a curved blade, getting the point in around a parry. This is subtle, but useful.

Again, these are all general pros and cons. The weapon's length, balance, weight, flexibility, and edge and point geometry all count in there as well, so before the pedants come crawling out of the woodwork, yes, I know there's a lot more to swords, but this is a solid, basic answer to why some people prefer straight and some prefer curved for different strengths and weaknesses which may be more or less important depending on the weapon's purpose.