Bobcat's aren't hard to kill, but #4 is too light to get through the fur and still penetrate enough for a quick kill.
BB, #2, 3, & 4 buckshot and such will work fine. The "heavishot" type loads are likely great, but I refuse to pay $3-$6 per shell for shotgun ammo.
I suppose that's one more reason why I use a rifle though.