The Dichlor will oxidize any bromide in the spa as well as the bromide added in the product to bromine. If you initially added any sodium bromide during startup, then you'll have bromide in the spa already. If not, then the initial uses of the brominating concentrate will produce a mixture of bromine and chlorine but over time the bromine will get used up and build up a bromide bank. So any oxidizer added, including chlorine, will create bromine.
Spa Essentials Spa Shock according to
this MSDS is basically non-chlorine shock (MPS) but with some additional trade secret ingredient. Spa Essentials Oxidizer Quick Clear is similar in that it is non-chlorine shock (MPS) but I can't find an MSDS so don't know if it has anything else in it.
In general, chlorine does a better job keeping the water clear than non-chlorine shock, but that wouldn't explain why Spa Shock works better for you since it doesn't list any chlorine in it (and the Trade Secret can't be chlorine).