Think it depends on if you want a higher chance of killing a bird, or if you're willing to sacrifice a bit but possibly bring in the biggest most dominant bird around.
What I mean is having a tom deke may scare away smaller birds that don't want a fight, but would bring in the dominant bird in the area.
So depends what your after, if you just wanna kill a legal bird I think your chances are better with just hens, maybe add a jake. If your determined to shoot a high scoring monster then use a tom deke, as long as you realize you may be sacrificing chances at smaller birds by doing so.