For every family, this is a personal, individual decision. There's nothing to prevent your parents from giving durable power of attorney for healthcare and finance to two different children. There's no right or wrong answer. It depends on your family and your situation. There may be a sibling in the family with whom everyone gets along. This conciliator may be the perfect person to have durable power of attorney for both healthcare and finance for your parents.
On the other hand, a lot of times, parents want their kids to act jointly. They want this to be a family decision and they want to ensure that no one feels left out. But one sibling may be good with numbers and money, and another may have the gift of caring, and so they want to give these responsibilities to different children, based on their skills. Likewise, some parents prefer a checks-and-balances approach. In such cases, dividing the responsibilities ensures that healthcare decisions won't be made solely on the basis of financial concerns.
Some attorneys will advise that you name one child to sign off on both health and financial decisions, while others advise that you name two. There's no blanket answer, and I try to talk to each family and explain what each role entails.
Remember that whatever your parents decide, they should draw up and sign the documents in the state in which they live, not where you live. State laws vary, and this will ensure that the document meets your parents' needs. If they move to a different state, they should draw up a new durable power of attorney for both healthcare and finance.
Additionally, consider registering these documents with an electronic storage service such as Legal Directives, which provides instant access to living wills, healthcare power of attorney, HIPAA releases, organ donation forms, hospital visitation forms, burial instructions, and more. If your parents are traveling and have an accident, these forms are available to health professionals and can ensure that your parents' wishes are followed.