I see now in the videos, yes I guess the bow is more powerful. I still think the shanks are more useful to a bear though for the reason Crim says.
As you can see in your other thread, the shanks give a defensive set bonus which makes them have higher armor and dodge, so if you are going to fight close up with the bad guys, better off having a set that has better armor and dodge. And obviously the difference in damage between the two is pretty small. The main advantage of the bow is to be able to attack from a distance which as Crim says, is not that useful to a bear as it renders much of the melee skill useless.
I do find it funny in the bow video how when you use the slash skills, the bear actually puts the bow in his left hand while he simply punches the Bandit Queen with his right hand. LOL