I encourage my clients to have BOTH a Durable Power of Attorney and a Healthcare Power of Attorney. Why? Because they cover two different aspects that will need to be covered should you not be able to make these decisions.
A Healthcare Power of Attorney addresses medical issues, and the person you select to make those decisions makes will ONLY be able to make healthcare decisions on your behalf.
A Durable Power of Attorney addresses more financial and business matters should you not be available to do so. The Durable Power of Attorney does not continue after death, however the person you select to be your durable power of attorney can be your executor and/or someone who inherits from your will. This person will not be able to make healthcare decisions for you.
The person you select for your Healthcare Power of Attorney can also be your Durable Power of Attorney, but BOTH documents are still needed for them to be able to do both.