1 kg cotton and 1 kg iron hit the head, which hurts?

It was hit.

First, the speed is the same;

Secondly, the stress area is required to be the same, so the shape of 1 kg cotton can be an extruded lump, and 1 kg iron can be a discus to ensure the same stress area;

The third mass is the same.

Then the momentum is the same, but the difference is the impulse. It takes a longer time for cotton to hit and rest than discus, so the force of cotton on the head is smaller, combined with the same stress area.

So iron hurts more.

The change of momentum is equal to impulse; Impulse is equal to the acting force times the acting time.