Governors have no better track record than senators at being president.
There have been very bad of both... Obama - senator, Carter - governor...
They do have something else in common though...
Going back to the 1920s (I don't recall when Senators started being elected by state popular vote rather than from the legislature), these served as Senators:
Obama
Nixon
Johnson
Kennedy
Truman
Harding
Govs. during the same period:
GW Bush
Clinton
Reagan
Carter
F Roosevelt
Coolidge
In spite of the list including Clinton, Carter, and Roosevelt, I'd have to go with Governors here.