Without hindsight: Barnes, because in spite of his sometimes excessively stubborn leadership style, he was a decent governor. Also, Perdue was openly courting the racist vote.
With hindsight: Barnes, for all of the above, plus the fact that Perdue had the unprecedented habit of always picking the state's "very optimistic" revenue forecast each year, thus circumvening the state's balanced budget requirement, plunging into deficits, and ruining the state's formerly perfect fiscal record. Also, if Barnes had been reelected, the Northern Arc might have gotten built.
How? I can guarantee in 2002 that he would never have gotten away with that.