The Ice Halo / Ice Halo HD are noticeably thicker than other protective headbands. The Unequal.com Halo headband is more like the Crasche headbands that I see more often at our rink. Unlike the Crasche headbands, the Halo doesn't seem to have as much protection for the back of the head.
One of our skaters used to have a soccer headband without the back-of-the-head protection. When they took a fall backwards and their head hit the ice, the headband literally popped off and gave no protection whatsoever.
I have several skating students who wear Crasche headbands, but they analyzed their options and chose that gear after discussing it for a while. The real beginning skaters wear skateboarding helmets, but you're beyond that level.
(Tip: the Crasche polka dot fabric cover is very cute. An adult I know had buyer's remorse, feeling it was too "childish" looking, so she barely used the headband.)