The office of Governor is extremely weak in Texas. You can thank the Reconstruction Republican government after the Civil War (or as we southerner like to say, the "War Between the States") for that. During Reconstruction the Radical Republicans took over the government in Texas and pretty much instituted Marshall Law. The appointed governor at the time, Edmund J. Davis, was a Southern Unionist who fled Texas after it joined the Confederate States and eventually became a Union General. A new constitution was written in 1869 that gave the Governor
power to appoint more than 9,000 offices, impinging on the independence of local government and the will of the people.During elections in 1873, Democrats won back many elected offices, despite intimidation by the State Police. The Governor's seat was won by Democrat Richard Coke, but quickly invalidated by the Texas Supreme Court (all Davis appointees). Angry Texans refused to accept the decision and when General Grant ignored requests to send federal troops to help Davis, he reluctantly stepped down. In 1876 a new Constitutional Convention was held, and devised a constitution that weakened the State Government to a shadow of it's former self.
Now the Governor's powers are limited to appointments to over 200 boards and commissions in Texas (approximately 3000 positions), mobilization of the Texas National Guard and Texas Rangers, and the line item veto. Just about every other office besides the board and commissions are elected by the People. The Governor has to be a very good persuader to get the Legislature (the law making and budgetary authority) to do what he wants, but he has no formal power over them.
Most appointees have 6 year terms and have to be approved by 2/3 of the Texas Legislature. Since a Governor's term only lasts for 4 years, if a new Governor is elected, he/she cannot appoint new commissioners, et.al., until their terms have expired. In this way, the former Governor continues his legacy.
Due to Perry's longevity in office (10 years, longer than any other Texas Governor), all of the boards and commissions are filled with his "Posse". This is where Perry's strength lies. He also knows how to game the system. If an elected official leaves office before his term expires, such as a Texas Supreme Court Justice (he's appointed 5 of them), Perry can also make an appointment to these offices. He also bent the Legislature to his will by vetoing 82 bills (more than any other Governor in a single session) in his first year in office, pretty much invalidating the entire session.
Other people have asked me why the Governor's office doesn't have term limits. (Perry has served 2 elected terms plus 2 years of Governor Bush's term when he left office to become President.) No other Texas Governor has completed 2 consecutive terms in office. So up till now, there has been no need for term limits. But, I have a feeling, that there soon will be calls for an amendment to the Texas Constitution to remedy this situation.
If Bill White gets elected, he will be starting from scratch, and may have to wait awhile before he can make any appointments. Also, since he didn't come up through the Legislature, he doesn't have the knowledge of the ins and outs of the system that Perry has. As a State Representative, Perry served on two of the most powerful committees in the legislature (Appropriations and Calendars) where he learned the importance of timing in the use of the veto.
So, if you want a super weak Governor, versus a semi-weak Governor, Bill White is your man.