I would think, given the state of firearms technology in the time of Henry VIII, that warbows would be far more effective for ship to ship close combat than the muskets of the day.
Possibly. But my point was that there were probably a lot fewer men around capable of handling the full-out warbows of a century before.
The 140 or so warbows on the Mary Rose varied in draw weight from 100 to 180 pounds, with most around 150/160.
Pulling a bow like this many times during battle, much less with enough control to hit anything, is not something one picks up in a few weeks of military basic training.
Only those who had essentially spent their whole lives training for this would have the physical strength, endurance and skill to do it.
My assumption, which is believe is pretty reasonable, is that there were a lot fewer of such men around in 1545 when the Mary Rose sank that at Agincourt in 1415.
The bow was no longer a dominating weapon on the battlefield, as seen by the English expulsion from France, so why would enough men pursue the lifelong dedication required to master it? Certainly not in the many thousands needed to field an effective army.
http://www.toxophilus.org/articles/anglais/mary_rose_en.html