If Bush is re-elected President then neither George or Jeb will be running for governor during his second term, IIRC George floated the idea earlier but was persuaded to drop it as they didn't want to give the appearance of using his father's position. That means the first gubernatorial elections that they can run in will be the 1998 Texas and Florida ones.
In our timeline George won on his first attempt in 1994 whilst Jeb lost – it often being blamed on his famous 'Probably nothing' statement. Does the extra age and experience allow Jeb to sidestep making a mistake like that? Ignoring the butterflies from Bush's re-election for a moment supposing that George and Jeb were both elected governor of Texas and Florida respectively at pretty much the same time, assuming that a Democrat succeeded Bush and served two terms which of the brothers does this put in the lead to run for President in 2004?
George W, simply because he is older.