Having trained with both for a very long time, under different teachers who came from different schools of thought, In the end they remain remarkably similar in principle, however they differ greatly in application.
I can tell you that I personally prefer the utility offered by the western pattern swords. The elongated quilions offer several advantages over the Japanese tsuba, as does the back edge and straight taper. Also, with small exception to some disarming techniques, Japanese schools do not teach techniques like half-swording or "wind and bind," which in historical context makes the longsword superior in its more dynamic application on the battlefield against armored troops. The Katana was a back-up weapon used in duels and indoor scenarios, but never as a primary. As Thom Noblitt has pointed out above: In war, that was a roll filled by the pike and spear.
Katanas do one thing well and with style: cut. But one should never say that the western longsword can't match it's cutting power, because it certainly can and often will if done with a well designed and well maintained blade.
In my circle (and I know many of you might disagree, but this opinion was formed by many individuals with years of experience) the Katana is considered sub par for practical use against anyone other than an opponent who is unarmored and equipped with a lesser weapon, because they lack good defensive options. Katana duels are often "fleshy," or in other words both opponents, Regardless of their mastery or skill, get mortally wounded (and Japanese schools often acknowledge that fact), as were a duel between two men with western swords are often less costly for the "winner" because of a more sound defensive/return capability offered by the long swords design and application.
I do respect the Katana, as I was first introduced to schools that practiced some form of Bushido, but It would not be my first choice for a personal weapon for the reasons I've stated above. However, In truth I would be hesitant to have a long sword fill that roll as well, regardless; though that is a whole new issue in its self.