Depends, both have different limitations and advantages. It probably was a combination of several things that lead certain people to favor certain technologies. It was probably a combination of armor and population pool. England had a decent amount of archers to already draw from. However the pool was shrinking or not large enough to accomodate the need as evidenced by the laws passed to make people practice archery.

Archery was never that popular among commoners on the continent. You only need to look back to EB times to see this. Romans employed Africans and Easterners to serve as archers. So if you're a continental country without a large supply pool of archers, without an large cottage industry capable of supporting the number of archers you need anyways, and you need a ranged unit... What is the best choice for you to make economically speaking? The easier solution of course, you train your peasants to be crossbowmen. You import the technical expertise from Italy so you don't have to develop the base and you get crossbow dominated armies which is a much better opportunity cost than starting from scratch. That or you just hire whatever mercenaries are on the market which would have been pretty light on trained bowmen but have a decent pool of crossbowmen.

Then of course there's the argument that mid-late medieval steel armors forced stronger bows which fewer archers could use that created an upper physical limit on the power of bows while crossbows could be mechanically cranked. And the crossbow more naturally segwayed into firearms.

A concrete timeframe would also help in this discussion...