Longbowmen are good for very specific situations. I once had a water channel one tile wide at times between me and Bismark. He warred me fairly on, right after he get a decent mass of his pikes. By wars end (which was 100's of years later, I think I had Arty by the time I crossed the channel and captured his cities) I had probably killed 50-60+ units with my Longbowen and Ship of the lines. Between him having his units embark stupidly (and this was before I realized I could just move on to embarked units to kill them) and the fact that he didnt build any range units, it was just an absolute slaughter. Was really fun to play though, realizing that I had maintained a good 20:1 unit kill ratio was awesome.
On the contrast, if your bows get stuck in forested terrains, with no good hills to sit on, there completely useless. if there arent any good choke points, it can be hard to get the concentration of fire you need. That coupled with the fact it takes 3-4 hits to kill units, means that if you dont get the right terrain\map layout, they are crippled. They are also arent very good at offensives at all, because you very rarely get to choose the terrain.