Most doctors agree that the most disabling joint should be treated first. The decision is more difficult if your symptoms and loss of function are equal between the arm and leg. In this case, several factors should be considered.
When the shoulder is replaced first, the knee must wait at least three months. This avoids putting weight on the shoulder. Sometimes, the second surgery must be delayed more than six months. This is the case when there are other soft tissues that are still healing.
The decision may be affected if there is any bone loss in either area. Severe bone loss may mean doing the operation in several steps or stages. Choosing the joint with the simplest operation may be a good idea. A faster recovery will allow you to have the other joint replaced sooner.