Asking Eric: One son is a better option to help in our retirement. How do we let the other down easy?

Parents are facing a difficult decision as both sons want them to move in during retirement. Due to the necessity of being closer to medical help, the parents must sell their current home and choose only one son. They are seeking advice on how to let the other son down gently and whether they are obligated to share the specific reasons behind their decision to favor one child over the other in this situation.