As far as "brakes" are concerned, you'll have more brakes with the hackamire that with the bit, because the horse is used to the hack. In fact, in general, a hackamor has more stopping power , I feel, due to the severe compression one can apply. Thus, it can be very severe, indeed.
See, here is the confusion at times for me
When the word 'hackamore' is used, western, it is synonymous with bosal, thus no leverage, and a horse can learn to run through a bosal more easily than a snaffle, and why old horsemen taught the double to a horse started in a hackamore.
A MECHANICAL hackamore, which I am sure you are talking about, can indeed have some very severe pressure and stopping power, but it ia leverage devise, and no where comparable to riding with a halter!
It is also why mechanical hackamores are not show legal, western, although many trail riders find them useful, and also gymkana people
You just cannot lump mechanical hackamores in with bittless devises that have no leverage , far as comments and function.