There is no difference between weapon types aside from the benefits they give you.
That being said, there are some benefits only wizard weapons (and magic source off-hand items) can give you, like +1 second to blizzard duration, or other specific things like that.
Around the end of normal mode, I found that a wand-source combo out-damaged anything else by a good margin, but at different points throughout the game, I've used 2-handed axes, staves, sword and shield combos, ect...
Weapon type does not matter, only weapon stats.
Just remember, weapon damage = spell damage, weapon speed = cast speed, crit chance = spell crit chance, and so on.
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