Power of Attorney takes effect during the incapacity of the person, and effectively ends if the person passes away. Power of Attorney is granted over all or some of the assets of the individual, unless those assets are in a Trust, in which case only the Trustee may make decisions.
A Living Trust on the other hand is amendable and revocable during the lifetime of the Trustor, however, it becomes non-amendable and irrevocable only when the Trustor passes away. If you are incapacitated or hospitalized, the nominated Trustee may continue to manage only those assets that are actually part of the Trust.
Both documents are extremely important and nominees holding the power of attorney should not be different than trustees of a living trust to avoid any issues and conflicts.
In short, the trustee of a Living Trust may administer only Trust assets during incapacity and after death.
The power of attorney nominee may only administer assets during the incapacity of the person, authority over which ends in death.