Neither one has more or less power than the other. A more accurate way to look at it is that they have different kinds of power—and are authorized to act at different times.
An agent named in a power of attorney document to handle another person’s finances or oversee medical care is authorized to take over these matters only while the person who appointed him or her is still alive. As another limitation, the agent can usually only act if the person is unable to handle those money and medical matters for himself or herself.
An executor, on the other hand, is the person named in a will to manage and distribute another’s property after death. The executor has no authority to act while the person is still alive—only to carry out the directions in the will.