Don't forget that an arrow coming off a bow has to go around the width of the bow (string on centerline, side of bow offset from that) so that arrow oscillates as it flies, reducing both accuracy and velocity at max distance.

As someone who's used a hunting bow (aaages ago) I can say it's quite difficult to master, as is slinging (long story). So, if you, as military leader, don't have a corps of already-trained archers or slingers, and don't have the years for them to learn, it's crossbows or muskets (well, or pole arms) .

That said, your chart on "works against armor" might need to change to "works against plate armor" - just think about the battle of Crecy (English longbowmen against French mounted knights).