Since nobody else responded, I'll offer my opinion. I don't think there is any reason you can't use different sanitizers in the pool and spa, but I personally would use dichlor (not trichlor if that is what you are using in your pool -- see other threads for why the distinction) to eliminate the need to stock two sets of chems and keep them straight.
Something else for theoritical consideration, but no practical concern... if you elect to use bromine, be aware that any bromine that travels from the spa to the pool on suits/hair etc will persist in the pool forever. That said, the concentrations will be so small that IMO it would take years before it even becomes measurable. Just food for thought.
While we are at it, one other pool/spa chemical issue is the use of muratic acid to lower pH. The amounts needed in a spa are so small that you are better off using sodium bisulfate to avoid overcorrecting.
