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That's an excellent question, and unfortunately I can't give you a totally satisfactory answer, like a link to a thread where there are records of comprehensive tests.
However, as far as I'm aware, there's never been any indication that the damage type of a weapon (burn/acid etc etc) makes any difference whatever to the amount of damage inflicted, or the hit ability of the weapon.
To think of if another way:
When a mob hits an avatar, the damage received is affected by armor (if any) worn by the avatar. As armor protects against specific damage types, the damage type of the mob is relevant.
However, mobs (so far as we know) don't wear armor (yet!), so the damage type of the avatar's weapon isn't relevant.