Saying a crossbow is better than a longbow or vise versa is a bit like saying a machine gun is better than a mortar. The fact is both remain in wide use by modern militaries, because they have different roles.
Of course there were crossbows and crossbows. They ranged from light weapons which could be used by anybody, to very strong weapons which were dangerous to play with unless you knew what you were doing.
In fact, one of the main reasons we don't know for sure about crossbows is that almost nobody can make replicas of the real military grade types from the Renaissance. There are only a handful of people around the world today who can make a 1200 lb draw prod. There aren't many of them floating around, and the antiques are too dangerous (and expensive) to play with. So nobody is really sure yet how these things perform, though I suspect we will find out in the near future because some folks have made some replicas in the 800 lbs range and are starting to do some preliminary tests.
http://www.youtube.com/watch?v=jdPyohqe7d0
On the longbow vs. armor thing. What you typically see are videos in which a super powerful 130 lb longbow is tried at ten feet against a 1.5mm thick munitions grade iron breastplate, which 'proves' longbows could pierce armor, then another video where an 80 lb longbow is shot at a 3mm thick tempered steel breastplate from 30 feet and the arrows all bounce of or shatter. Thus "proving" longbows couldn't pierce plate armor. Few people who do these tests really want to know the reality, and they generally serve to further muddy the waters. Hence the debate rages on into infinity, like so all our political debates....
G.