Apparently, it doesn't matter which army you use to attack it; a script triggers, and you receive the (small) troops that are specified in it.
I specifically tried gathering more troops after my first attempt, but it turned out to be useless.
Defeating the bird isn't that difficult if you cast the "weakness" spell on it and maintain it throughout the battle.
Then it attacks much weaker, and the army you receive is more than enough to win.
And don't forget about the tree.
:)