PORTSMOUTH, N.H. — Jeb Bush and Marco Rubio are on course for a collision.

There once was mutual public deference. But that has eroded as the Florida Republicans battling for the presidential nomination have come to see the other as the main threat to lofty ambitions: Bush claims the party establishment’s mantle, Rubio wants to be the party’s fresh national face.

Bush now routinely compares Rubio’s background to Barack Obama’s before the Democrat became president. Rubio says it’s “time to turn the page,” a reference that strikes as hard at Bush’s long family legacy as it does at Democrat Hillary Rodham Clinton.

The rise of GOP outsiders such as Donald Trump and Ben Carson has increased the stakes for Bush and Rubio as they try to become the mainstream alternative. Whoever wins this internal contest will show whether experience or fresh leadership is the bigger priority for GOP centrists.

From Bush, there’s a sense of urgency in his contention that Rubio, in his first Senate term, has not proved his leadership credentials. The ex-governor and his team are frustrated, too, that this shortcoming they attribute to Rubio has not become more of a liability for him.

It’s part of the mantra Bush has repeated since the Republicans’ second debate in California a month ago, when Rubio won praise for staying above the fray. He has since drawn nearly even with Bush in national polls, although both remain in the high single digits.

“We’ve got a president that the American people supported based on the fact that he was an eloquent guy,” Bush said in Iowa last week. “And he had nothing in his background that would suggest he could lead.”

Though describing Obama, it’s a slight to Rubio. He delivers a compelling story about his parents’ flight from Cuba and his working class background, but he has been in the Senate less than five years and has missed much of its business this year while campaigning for president.

Evidence of the tension between the Florida politicians was on display Thursday when Rubio’s campaign, minutes after the Bush organization announced raising $13.4 million in the last quarter, boasted it had more cash on hand. Rubio reported having nearly $11 million in his coffers compared with Bush’s $10 million. But about $1 million of Rubio’s cash cannot be accessed unless he wins the GOP nomination, a point Bush campaign spokesman Tim Miller pounced on via Twitter.