You attack slower with swords than with only your fists, how much slower depends on the mass and size of the weapon. Bigger weapons tend to do more damage if you can use them successfully though.
Swords work fine, but without skill in the art of using it, you will do little damage, you have to train sword skill to get good damage with the swords.
Axes seems a little faster than swords, but also seems to do less damage(but I haven\'t used axes in a while so I am not sure if this still apply)