i did this before but i was a noob and didn't do any pictures or anything an it just wasn't a good thread. but its dead now so here is a better version!
so here is what you do. 2 warriors fight in a one on one battle in flat terrain they are both equally skilled and have no armor but they have different weapons you vote on which one would win.
I don't have much recollection of a war hammer actually ever being used. It would be more of a mace if anything.
Well then, read and learn. The war hammer in its different forms was used in medieval times by different units. From the Horseman's pick over the maul up to the pole weapon Bec de corbin, it is definitely not only a mace-like weapon.
A battleaxe is certainly a powerful and stylish weapon, but I think I am going with the warhammer. Contrary to battleaxes it was even effective against the toughest of armors.
Warhammer wins every time. Enemy has some armor on? No problem just crush it and his organs. His armor to thick? Physics! The power will transfer through his armor into him! The weight and length give the hammer the momentum and swing to become devastating.
longbows are better weapons but it takes much longer to teach someone to be good with a longbow. It takes much less time to teach someone to use a crossbow so in times of war you can deploy much more crossbow men than you can longbow men. I vote crossbow