All gamemodes are flagged as the type "gamemode". This means when you use the command "gamemode " it will auto stop the previous gamemode, and start the new one. This is not the case if you use the "start" command.
Unfortunately, broph is not marked as a gamemode (mainly so that people cant vote to play it), since its more like a sandbox environment.
In other words, if you had the gamemode "stealth" started, you could do "gamemode cdm cdm-ls" which would stop stealth, and start CDM. Broph is an exception, you need to start it using "start broph", and the gamemode command wont stop it, so you need to do "stop broph".
I hope that answers your question.