Well dog aggression and human aggression are two differnet things and its very smart of you to ask. You can never say for sure what will happen but let start with some background. Regardless of the follwoing they will NEED to be introduced in a neutral territory like a park. Their food will need to be seperate, seperate rooms if possible and should NEVER be left alone.
Your Dog
How old is your dog?
Is your dog male or female?
Is your dog spayed or nuetered?
Where does your dog spend most of its time?
Brother's Dog
How old is the pitty?
Is it male or female?
Is it spayed or neutered?
Is it crate trained?
Its not a impossible situation since its temporary. When neither of you are home they NEED to be seperated whether its by a room, one is crated, or one is outside. Dogs become jealous and territorial that is why I say they need to be fed seperatly. Also most pitties dont get a dog aggression issue until after they have passed their puppy phase. If this dog is under a year old the potential for a issue is slimmer then if it is older.
I'm also not saying that they wont get along but precautiones need to be taken, plan on it being a large adjustment and if good things do happen then you can say that you at least planned and were prepared for a hassle.
As a pit bul lowner I have come across a huge number of otehr pit owners who fight so hard to break the stereotype that they ignore the potential in their dog, convinced that the love they have gaven them surpasses instinct. I'm not saying your brotehr is such but if he comes at you with a attitude that his dog would NEVER harm a fly then you know to be more cautious. Onthe other hand nobody kows this dog more then your brother so basically dont panic but be aware. If a dog is outta its element and is under stress (which any home type of move will inccur) it will react differently then maybe your brother has witnessed
It may very well be that his dog would never start a fight, could very well be the nicest dog EVER as many pit bulls are BUT that dosnt mean it wont finish a fight. My girl is VERY well behaved, very submissive to other dogs, and I ahve not seen a ggressive bone in her body but just knowing her protective instinct I am always on guard when there are other dogs around.