Republican Sens. Ted Cruz and Rand Paul both tapped into the powerful Tea Party movement, fueled by frustration with big government and overspending, to win their seats in Congress. 

Now, the two freshman senators find themselves competing directly for that same constituency as they seek the party nomination in the 2016 presidential race. And the Tea Party wave -- which Paul rode in 2010, followed by Cruz two years later -- may only be big enough for one of them this time around. 

Paul, on Tuesday, formally announced his presidential bid, vowing to "take America back" and wielding a "message of liberty." In a fiery speech tapping into the same kind of Beltway frustration that boosted Republicans in 2010, Paul blamed both parties for Washington's dysfunction. 

He and Cruz are now the only two announced candidates on the field. Though neither has come out brawling, an evident Paul-Cruz rivalry has simmered in recent months and is sure to grow as primary season gets underway. 

The two so far have politely sparred, with Paul, of Kentucky, recently questioning whether Cruz’s message is broad enough to win.

"I guess what makes us different is probably our approach as to how we would make the party bigger," Paul told Fox News after Cruz, of Texas, officially announced his bid in late March. “Ted Cruz is a conservative, but it also goes to win-ability. And people will have to make a decision, which is the Republican who can not only excite the base but also bring new people into the party without giving up their principles." 

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On Tuesday, Cruz was cordial, saying he respects Paul's "talent" and "passion." 

Cruz and Paul unsurprisingly agree on most issues -- from overhauling the federal tax code to repealing ObamaCare.

But the point where they diverge appears to be at the water’s edge of American politics.  

"I'm a big fan of Rand Paul,” Cruz, considered more hawkish than Paul, recently told ABC News. “He and I are good friends [but] I don't agree with him on foreign policy."

To be sure, they clearly disagree on President Obama’s decision last year to restore diplomatic relations with Cuba.

At a recent summit in California sponsored by the Koch brothers-backed Freedom Partners, Paul argued that a half-century of economic embargoes have failed to remove leaders Fidel and Raul Castro. 

But Cruz, a Cuban-American, said at the time: “The Castro brothers are brutal dictators.” 

They have also disagreed on the tentative nuclear deal signed last week with Iran, though Paul now appears to align himself more with fellow Senate Republicans.

“This is the worst negotiation ever in the history of mankind,” Cruz said at the California summit (held before the deal was announced), warning of an Iranian nuclear strike in Tel Aviv, New York or Los Angeles.

Paul urged Cruz to have patience, asking, “Are you ready to send ground troops to Iran?”

However, Paul later joined Cruz and 44 other Republican senators in signing Arkansas GOP Sen. Tom Cotton’s letter to Iranian leaders saying a final deal must have congressional approval and suggesting one with Obama could end when he leaves office in January 2017.

And while Cruz and Paul differ on some foreign policy issues, they are surprisingly close on others including support of increased defense spending, which Paul formerly opposed, and arming Kurdish forces in the fight against the Islamic State, instead of sending U.S. ground troops to Iraq or Syria.

“The only people over there that can fight and have been showing some ability to fight are the Kurds,” Paul, who says he has been mischaracterized as an isolationist, recently told Yahoo News. “I would fund them directly.”

If Paul has an advantage within the party base, it is most obviously with the libertarian wing of the party, considering he continues to champion the ideals of individual liberty and less government put forth by his father, former presidential candidate and retired Texas GOP Rep. Ron Paul.

"Cruz and Paul must both appeal to the conservative wing of the GOP," David Payne, a Republican strategist and a senior vice president at Washington, D.C.-based Vox Global, said Monday. "But Paul also relies on a lot of excited primary voters who don’t call themselves 'conservative Republicans.' Consider all the libertarians or isolationists or younger political activists he can rally to his cause. This is his advantage over Cruz. .... Rand Paul is positioned to talk with the conservative GOP base while also expanding upon it more easily."

Paul supporters do not appear concerned that he could lose such backing in an effort to appeal to more primary voters.

“Rand Paul and his father each attract new people to the party in their own unique ways, yet they both share a deep passion for liberty,” Rand Paul Victory Committee spokesman Sergio Gor recently told The Washington Post. “Among the thousands of people Sen. Paul meets every month, the most enthused and energetic are usually those individuals who supported his father. The same individuals continue to stand with Rand.”

Cruz, a Southern Baptist and the son of preacher, has made faith a big part of his personal and political life and is clearly focused on winning the evangelical vote.

“God's blessing has been on America from the very beginning of this nation, and I believe God isn't done with America yet,” Cruz said on March 23 in announcing his candidacy for president, at the Christian college Liberty University, in Lynchburg, Va. “I believe in you. I believe in the power of millions of courageous conservatives rising up to re-ignite the promise of America.”

He also chose Easter weekend to run his first ad of the 2016 presidential election cycle.

“Were it not for the transformative love of Jesus Christ, I would have been raised by a single mom without my father in the household," Cruz says in the 30-second ad. “This is our fight, and that is why I’m running for president.”

The Associated Press contributed to this report.