Fire

First, the info that I am presenting comes from my personal experience as a professional sword merchant, from my experience as a sword smith, and from my years of experience with european and eastern martial arts- this debate has gone on for many years, and will, I am sure, continue- up untill the end of the sword as a battlefield weapon shortly before world war one, everyone that had any vested interest was still trying to build "the ultimate sword"
ultimately it has broken down to the realization that no one blade can do it all, and a series of specialized weapons and compromise pieces- as to the superiority of one type of blade for cutting, that depends on the type of cut- curved swords excell at draw cuts, where the blade is moving backwards or forewards as well as slashing through- a purely straight blade is good for a shear cut , or straight chop, but overall not a great cutter- In the tests that I have conducted, on nearly 50 different swords, a slightly curved blade, like a katana will cut deeper and more effectively than a straight blade- we test on a variety of substances, from a large stump, to tree branches, to heavy carpet tubes, to two by fours- we try to run a sampling to get a fair idea of how the stuff that we make and order for resale performs under realistic conditions- the straight blade will cut fairly well, but if it encounters a bone it will tend to shear it, or break it, while the curved blade will tend to slash through it more cleanly- really it has to do with angles and physics- and this is why every slashing impliment from a machete to a katana tends to have a slight curve to it- it is simply better at slashing, as milenia of experience have shown- too much curvature is not a good thing, as it will tend to skate off, as shakran mentioned, instead of bite deep- the scimitar, mentioned above, is and always was a horsemans weapon- many horsemans swords exhibt a deeper curve (you see this in 1800's calvary weapons as well) to help them slide past, even if they skate off some, as it is vital to prevent them from binding and being wrenched out of the users hand on a ride by attack- Knights swords avoided this for the most part as they always were geared to fight other knights, and had to contend with heavier armor, and toward the end tended to drop swords altogether in favor of picks and maces and hammers- a straight sword can be made to cut better if it starts with a sufficiently wide blade and tapers sharply- or if it compensates with a broader blade and consequentialy more weight- but this still will not generaly overtake a blade with a slight curve, provided both are well made and equally sharp.

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Thought the harder, Heart the bolder,
Mood the more as our might lessens