Plumed Archer vs Crossbow

I just had a closer look at the plumed archers and I wonder why they are worth the higher cost compared to crossbows. They have 1 more pierce armor but 1 less attack. Every general guide I watched told me to get the attack upgrades for archers first because they need attack more than armor. Isn’t in castle age pierce armor pretty much irrelevant anyways since mangonels are a bigger threat to archers? Okay, PAs have 50 HP so they survive one mangonel shot, but if you face a single mangonel crossbows can take it down pretty quick. PAs also move faster, but is this really so strong? I can see that players with good micro can hit and run skirms and dodge mangonel shots easier with the higher moving speed, but does it matter on lower elos?