Hot tub chemical stores always tell you to use bromine instead of chlorine. They claim chlorine will destroy your tub. I have been using chlorine for 20+ years on 3 different tubs. Never had a problem. I suspect they recommend bromine only because it’s more expensive.
Bromine has a higher boiling point than chlorine, which allows it to stay in the hot water longer. You can use chlorine in a hot tub, but you have to add it more frequently to achieve the proper level of sanitization.
It’s a matter of long-term economic effect. Both work, but one is cheaper in the long-term because bromide sanitizers for longer at higher temperatures, such as those which exist in hot tubs. That’s the point they were making.
Chlorine also works fine, but because of the higher temperatures, you have to use more, which cost more.