Light crossbows had at least twice as much draw force (>300 lbs) as longbows since you can use your legs or a winch, etc. They'd do in a target in chain but not plate. Heavy crossbows (arbalests) had 1000+ lbs draws and would deliver a bad day (though not necessarily fatal) to a target in plate. Longbows had ~150 lbs draws and were for lofting at 45 degrees and killing un/light-armored guys 200-300 yards away. They just don't pack enough punch to go through plate.
Hand-to-hand, you're right about hammers and picks.
Muskets are the primary reason that heavy armor went out of style pre-Renaissance. Give a peasant a gun and some practice and your expensive highly-trained noble-born knights are dead 100% of the time before they can get in range.
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