My experience has been that these three centers have physicians with unique special interests. I try to direct people to the physician and center that best matches their medical issue.
In some areas, the three centers also differ in organization. For example: At Mayo Rochester, the ascending aortic aneurysm surgeons are also transplant surgeons. I don't know what their ties are to the Aortic Center itself, which does descending and abdominal aortic aneurysms.