I have used both cones and the shackles. They will flap themselves out of the cone unless you hold them by their head. They won't do that with the shackles. BUT we had 4/20 birds break wings while flapping in shackles, so purely personal preference. Shackles seem very slightly faster and more efficient because if you have multiple you can quickly move from one bird to the next.
I've only used the broomstick.
But my wrists have taken damage since then and I'm not sure I could hold on to a sizeable meatie.