In the basic D&D book it says a crossbow quarrel does 1d6 damage.
On this site http://www.mjyoung.net/dungeon/char/weap033.html
It says a quarrel from a regular crossbow does 1d4 dmg
While a quarrel from a heavy crossbow does either 1d4+1 or 1d6+1.
I submit to you that in our game:
regular (light) crossbow: 1d6
heavy crossbow: 1d6+1
This rumour I heard about a heavy crossbow doing the same as a battle axe is BULLSHIT!