A Dwarven Crossbow has higher damage than any bow in the game, Daedric or otherwise (base damage is 3 points higher than a Daedric Bow). Even the weaker crossbows have the same base damage as a Daedric Bow.
You are right, I should have done some research before making such a quick assumption, I am incorrect, which also means OP (
berzum) is incorrect in saying,
However skyrim seems to me that crossbows fire slower and do less damage, while bows fire faster and do more damage with one arrow, WTF why did they make it this way?
Berzum - you have your conclusion, based on statistics, crossbows = higher damage, slower speed whereas bows = slightly less damage, faster speed. Choose based on your personal preference.
Instead of making a whole post about a basic question, perhaps you should try
http://elderscrolls.wikia.com for a quicker, easier way to find the answers you need about the game. I'll take my same advice when responding.