I don't have the screenshot results at the moment, but I was doing some testing with crossbow units vs longbow units.

To do the testing, I let one be defensive, and one attack (because it makes sense in-battle)

Initially I tested Retinue Longbowmen against Geneose Crossbowmen (arguably the best of each), and let them duke it out. I set the player-controlled group as the longbowmen, set them up as loose formation , guard mode and let them auto-fire. Initially they make some early kills against the Genoese xbowmen while they set up and moved to loose formation. As the fight wore on, the xbowmen kills increased while the shields on their backs became telling. Eventually the Longbowmen ran out of ammo with fewer men. The Genoese Xbomen won out (I tested it twice and the second time it was even worse for the retinue longbowmen)

I then used the French Aventurier's as they are just armored but without any shields, just to see if its the shields that really mattered. Nope, the battle was closer but the extra "punch" of the Crossbows really showed through. Again I tested twice and it came out as an "Average Defeat" for the Longbows.

I'm going to remind you that I DID have the Longbows already set up in loose formation, and firing first so if I switched positions, it would be even WORSE for the longbows.

I then scrolled through the different factions and found that Dismounted Dvors for Russia seemed to have the highest missile attack (11) out of any archer unit in the game. I did the same test and it wasn't even a contest Dvors lost)

I did these tests because of another thread where we compared units and I stated I loved Pavise-style xbowmen, but others kept spouting the benefits of Longbowmen.

When you think about it, longbowmen were prized due to their fast reloading skill, not their "punch". That's not to say longbows didn't have a "punch" but they obviously cannot beat out crossbows for "punch". M2TW isn't really that realistic because most armies back then probably were comprised of mostly peasant armies who (if armored) wore leather or padded armor. Longbows would be easily effective against that, and if you can spam missiles against mostly peasant armies its more effective than the slower reload of crossbows (which would be more effective against heavily armored opponents, which you probably didn't see as often).