Not exactly the same topic, but pretty dang close. We just beat this topic to DEATH on the small game and predator page of the forum...

17hmr 22mag coyotes under 100yds

Ultimately, if it's LEGAL, and you can make a head shot, then either are great for birds. Hit a bird on the ground in the head with a pellet from a BB gun and he's going down, but that's not to say I'd personally pursue that technique.

For headshots on birds, the .17HMR offers a flatter trajectory, and plenty of power to pop a top. The flatter trajectory is the benefit of the .17HMR on small game (or headshot birds), whereas the heavier bullets of the .22WMR are a benefit when you're talking about larger game, like fox, bobcat, or coyotes, otherwise, the two are pretty similar in killing performance.

Keep in mind that shooting for their HEAD isn't an ethical shot. For birds, you need to be shooting for their BRAIN. The problem with that is that they call it "bird brained" for a reason. Their actual brain is VERY small, making a CNS hit actually quite difficult.

Again, personally, it aint my bag. Wing shooting with a shotgun doesn't ruin THAT MUCH meat that I'd say rifle hunting is a better idea. I HAVE seen wounded geese with their bills blown off, I'm assuming by someone shooting at them with a rifle, they can still fly and escape, but they can't feed, so they either die of starvation or infection, either way, it's not a pretty sight, and not what I'd call "ethical pursuit".