Gaining the title is more or less what Sora said it was: a formality. It's to show to other wielders that you have gained notoriety for your skills, but any benefits a master receives depends on what "school" they went to. From what we've seen, wielders loosely form their own groups with their own ways of teaching and secrets. Like at Land of Departure, Master Eraqus has his own way of teaching and he expects his students to follow that line of study to a T. Aqua met those criteria so along with the title of master, she was rewarded with the secrets of the land and inherited Master Eraqus' Keyblade, Master Keeper. Those were benefits exclusive for training at Land of Departure.
It all comes down to where someone graduates if a master gains something after their training, if anything.