API-650 5.9.1 says that stiffening rings shall be "preferably on the outside of the tank shell". That wording implies to me that they CAN be put on the inside if there is some good reason to do so.
From a design standpoint, it doesn't matter if they're internal or external.
Of course, if the tank has an internal or external floating roof, or if it is considered possible that it might ever have one in the future, any stiffeners would be external. Owners, inspectors, painters, will be used to seeing them outside, not inside. Interior stiffeners introduce some different corrosion considerations. Location of stiffeners may have some impact on erection costs.
