I would be inclined to say that Western Martial Arts are every bit as applicable to a modern combat situation as Eastern Martial Arts, which is just another way of saying what almost everyone else here has said.
I think the usual advantage for a swordsman is that he has a shield or dagger in the other hand. I wouldn't expect someone armed with just a sword to do well against someone armed with a spear. Does your spear vs. sword experience involve off-hand items for the swordsmen?