Articuno's the worst of the legendary birds, because pretty much anything that can take Ice Beam and has Rock Slide can take it out. Heck, an Octillery with Rock Blast can take it out! But it does have it's advantages, such as stalling pretty much every water type out there, absorbing Sleep Powder and Spore, and nullifying Snorlax. But it takes some prediction to use correctly.
Zapdos is the best of the legendary birds, because it doesn't have a 4x weakness to Rock types, like the other two do. It has the highest Special Attack stat of all the legendaries, along with Moltres. Send it out with a Special Sponge, and it'll devour an entire team!
Moltres, obviously, isn't as good as Zapdos, but it's better than Articuno. It has the highest Special Attack stat of all the legendaries, along with Zapdos. Use Sunny Day, and it can inflict heavy damage on all kinds of stuff.