I had a Lab/pit mix (also a rescue dog, ~50 pounds full grown) who lived to be 16 and was smarter than several people I know ... I agree with others who have said that socializing and training is important. She was definitely the alpha (or tried to be) in her dealings with other dogs, but loved to be around people and other animals. We introduced another (and much smaller) dog into the family, and they had one scrap in eight years, over food. Once they figured out who was in charge, they were inseparable.
Starting when she was a pup, I made sure to mess with her while she was eating, take things from her mouth, play with her paws, etc., but I've done that with every dog I've had. She had a crazy food drive, and would stop at nothing to get at trash, food on the counter, etc., but not sure that had anything to do with her breed.
She was a great dog and companion, and I wouldn't hesitate to get a similar mix again, provided they were personable and sweet when first interacting with them. (Again, as with any breed.)