John,
It is several years now that I receive Privigen during September-April and Gammagard during May-August.
This is not my choice, really; it's just that the infusion center in one location has an arrangement with one company (Behring) and the other infusion center I go to in another location has it with another (Baxalta, a spun-off from Baxter).
Despite my concerns, I have not had any problem going back and forth from one brand to the other.