I don't understand why crossbows aren't more popular.
Pope once banned crossbows because they are just too much. Nobody ever banned katanas... And if the Pope had ban katanas, it means that they are cool like condoms and gay-marriage. Katanas however belong to the less prestigious non-banned category.
Actually, they got banned mostly because they were a pre-gamebreaker
Finishing off a knight was a really mean feat. You'd rather beat him silly and capture him, getting his stuff and a hefty ransom afterwards from his family.
Bows - well, bows were mean. Very hard to impossible (as armour form changed) to do something to the knight, but the horse would have it tough. But it was still cool, using a bow is quite hard. You'd need a lot of effort to train your infantry with it (hence the bow tournaments organized by medieval guilds) to a half decent level, and you'd need to build cultivating this skill into the very core of culture of a nation to use it to it's full potential (England actually managed to pull this one off).
Now a crossbow? You don't need
half as much strength*, and only a percentile of time you'd have to spend on learning to fire a bow. And because you can make it more powerful, you really don't need as sophisticated ammunition.
*I've always found baffling the fact that most RPG's either ignore this or even flip it around. I've never fired a crossbow heavier than 4kg - and it had about 130 kg's of pull on it's bow, and
lot's of ornaments. With kinda weak, 25-kg bow, you have to hold this strength in
your fingers.
As to what's better, katana or a longsword... Well, in the very unlikely event that a knight would face off a samurai - I'm not sure why they'd use their secondary weapons first (or is it tertiary for samurai?). It was largely a "braggin rights" weapon for both, so if it went to trashtalk it could play a role. But still, who'd win? Katanas have bigger mystique, what with cutting the leaf on water, but then again, longsword is not only longer - but also broader. Wait, scratch that - it's an anachronism, a knight would not crack double entendres.
I still like European swords better, especially the bastard, but maybe I'd feel different if I trained kendo, or something.
@ Dausuul: well, maybe not katanas, but other slashing weapons, sure. It's a well established standard to use some kind of slashing weapons when you're not facing heavily armoured opponent - see sabres, scimitars and such. A notable exception to this was a rapier, a exceptionally deadly weapon (which was why in rapier-wielding western Europe, duels were banned much sooner than in sabre-using eastern Europe). Sabre holds much more "stopping power", but with rapier - you can loose the duel, and have the opponent die nevertheless from a fatal internal injury you've dealt in one of the early blows. Not very reassuring when your goal is to live through, but still - it shows how different approach can sort of work.