My cats love the DaBird, too. I have to patch it up regularly. I bought a pack of feathers at the craft store to replace those that get chewed-off during play and it's got duct-tape all over it by now to hold it together.
They are typically pretty good about taking turns. When the bird is "flying" Mikesch will jump and twist and turn to catch it and Binky will watch. When I drag it over the ground, most of the times Binky will pounce on it and Mikesch will watch. I haven't heard them hiss at each other yet. Actually, just the other day, Mikesch caught the bird in the air and then placed it on the ground in front of Binky's nose to share his catch. So cute! Sometimes though when he catches the bird, he'll grab it tightly in his mouth and run off with his "prey" to his "cave" to hide it and chew on it. Hence the necessity for frequent repairs...