What is one power that most governors have that the president does not have?

Governors can veto state bills, but nothing besides a state bill. The president has the power to veto any law or bill that is present.

The president can veto only a federal bill, one that was passed by Congress, and he can only veto the entire bill -- he can't pick the parts he likes and dislikes.

Governors can veto only state bills, passed by that state's legislature. Some governors have the line-item veto. They can veto the parts of a bill they object to, and let the rest become law.