Washington (CNN) Donald Trump says he has "far better judgment" than Republican presidential rival Ted Cruz after recordings revealed the Texas senator questioning the Republican front-runner on that subject.

"I was against going into Iraq," Trump told CNN's Jake Tapper in an interview that aired Sunday on "State of the Union." "That's good judgment. I was for bombing (ISIS's) oil long before anyone else was talking about it. That's good judgment. I have great judgment. I would say I have far better judgment than Ted."

The unusually cordial relationship between two of the top contenders for the GOP nomination fractured late last week and appears to be entering a new phase.

Their sparring is likely to intensify given the results of the latest Des Moines Register/Bloomberg News poll Saturday showing Cruz surging ahead of Trump in Iowa, 31% to 21%. The two will face off Tuesday in Las Vegas at the next Republican presidential debate, sponsored by CNN.

"He's been so nice to me. I mean, I can say anything, and he said, 'I agree, I agree,'" Trump said. "But I think the time will come to an end pretty soon, it sounds like."

Fulfilling his prediction, Trump called Cruz "a little bit of a maniac" in a separate interview, aired on Fox News Sunday. He criticized Cruz's history of intra-party squabbles -- including calling Senate Majority Leader Mitch McConnell, R-Kentucky, a liar.

"You look like the way he's dealt with the Senate, where he goes in there like -- frankly like a little bit of a maniac. You're never going to get things done that way," Trump said.

"You can't walk into the Senate and scream and call people liars and not be able to cajole and get along with people," he said. "He'll never be able to get anything done, and that's the problem with Ted."

Last week, The New York Times released audio of Cruz speaking at a private fundraiser, where he questioned Trump and Ben Carson's judgment to lead America.

"You look at Paris, you look at San Bernardino, it's given a seriousness to this race," Cruz said. "People are looking for who is prepared to be a commander in chief. Who understands the threats we face. 'Who am I comfortable having their finger on the button?' Now that's a question of strength, but it's also a question of judgment. And I think that is a question that is a challenging question for both of them."

Trump said his professional success proves that he has "great" judgment.

JUST WATCHED Can Ted Cruz beat Donald Trump? Replay More Videos ... MUST WATCH Can Ted Cruz beat Donald Trump? 02:26

"My judgment is great. I built a multi-, multi-, multi-billion-dollar company. Some of the greatest assets in the world," he said. "Tremendously big, number one bestsellers, including "The Art of the Deal," which may be the best in terms of business books. Tremendous television show called the Apprentice that lasted 14 seasons, and by NBC came -- they would beg me to do it again, as you can imagine and I said no, and they are going to sign, they signed Arnold Schwarzenegger."

Trump also praised his "strong temperament."

"One of the things I have is really good judgment, and I think I have really great temperament," he said. "It's a strong temperament, but you know when they chop heads off of Christians in the Middle East, and other people also. When they chop off heads, and when they treat people the way -- we're like Medieval times. Having a strong temperament is good."

Trump told Tapper that voters should pick him over Cruz because he's "more capable" to lead the country and that he gets along with people "much better" than Cruz.

"I'm more capable. Because I have a much better temperament. Because I actually get along with people much better than he does," he said. "You know people don't know that about me -- I actually have a great relationship with people. In fact, I was criticized in the beginning because I get along with Democrats and liberals and Republicans, and conservatives -- I get along with everybody."

Cruz, on the other hand, does not get along with everybody, Trump said.

"No, I don't think he does, and I like him," he said.