I'm not entirely sure on numbers, since it can vary on the mob.
In some experiences, I out-aggro a bird on bosses, especially when I'm able to do all my slashes and combos.
In pvp, I've tried killing a bird (not sure if he was full dex), in 2 normal shots with a hammer.
IMO, if the warbird has damage gear on, you might be at par or you just a little bit on top. If its a tank warbird, definitely you are going to deal more damage.
The only time I usually get more damage than a dex bird is when I have rage on.
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