I think the ones really enjoying this kind of weapon were the Polish. Here says that inventories give near parity with broadswords (sabers?), as the weapon to be used after a lance charge.
http://www.kismeta.com/diGrasse/Koncerz.htm
About crossbows and bows losing ground to fire weapons, what it is often not realized is that you can have a bag with a kilo of arquebus balls and that will give you some 40 shots. But to have 40 arrows or bolts is much more encumbering. So the rate of fire is secondary. Of course, you can recover some, but only when the fight is over...if you win.
In his memories, Marshall Monluc describes how he became behind the Spanish lines in Fuenterrabia in 1521 with a band of crossbowmen for a couple of days. Trying to return they were very afraid of encountering Spanish cavalry because their bolts could not penetrate and they were wasting them fast. Their only hope was a small group of Navarrese shotgunners. 4 years later at Pavia, the French were still hardly using arquebuses.