AUSTIN, Tex. — Gov. Rick Perry, a Republican contemplating a presidential run, shares many attributes with the last man who ran for president from here, his predecessor and onetime patron, George W. Bush. He has the same straight-legged Texas swagger; the down-home, clipped speaking style; the desert-baked conservatism.

But in recent years, Mr. Perry has broken politically with Mr. Bush, questioning his credentials as a fiscal conservative, accusing him of going on “a big-government binge” and playing down some of Mr. Bush’s accomplishments in Texas in light of his own.

Mr. Perry’s public statements exposed a long-simmering rivalry that had been little known outside the political fraternity here but underscores the rightward drift of the Republican Party since Mr. Bush was president. More acutely, Mr. Perry’s criticism holds potential peril and benefit for him should he decide to mount a presidential campaign, allowing him to establish an identity distinct from Mr. Bush but risking a guerrilla campaign against him by the former president’s inner circle.

Mr. Perry, who aides say will make a decision within weeks, has been meeting around the country with potential fund-raisers, went to Colorado last week for a gathering of prominent conservative rainmakers held by members of the Koch family, which helped finance the Tea Party movement. An inevitable question is whether Republicans will be willing to nominate another Texas governor so closely connected to the last one.