"I betcha I'd have more endurance," she told Runner's World magazine.
"My one claim to fame in my own little internal running circle is a sub-four marathon" in Anchorage, she said, referring to her 2005 sprint in the Humpy's Marathon in which she beat the four-hour mark by 24 seconds. "What I lacked in physical strength or skill, I made up for in determination and endurance," she said.
The president, who stays fit by starting his day with a workout in the White House gym, is better known for his passion for basketball and has been a frequent golfer in recent weeks. Obama, however, recently acknowledged that he hasn't completely kicked his smoking habit, telling reporters that he does still "mess up" on his pledge to quit smoking.
Might Obama join the workout war of words? A message seeking comment Tuesday from the White House by The Associated Press wasn't immediately returned.
Palin, a 45-year-old former beauty queen who became the first woman and youngest person to be elected Alaska's governor, is featured in the August issue of the magazine for running aficionados. She was dubbed the country's "hottest" governor when she stole the show as U.S. Sen. John McCain's presidential running mate in 2008.
In the interview, she talks about her fondness for running, which is perhaps why the mother of five who gave birth to a baby boy last year is able to keep trim. The magazine on Tuesday published an extended version on its Web site.
Palin said the exercise wasn't just a body thing and that it helps keep her emotionally and mentally in shape.
"I feel so crappy if I go more than a few days without running. No matter how rotten I feel before or during a run, it's always worth it to me afterward. Sweat is my sanity," Palin tells the magazine.
She said one of her biggest frustrations while campaigning with McCain was that the senator's staff didn't carve out time for Palin to get in a jog. But she recounted one memorable run at McCain's ranch in which she fell coming down a hill. The incident happened a few days before the debate with now Vice President Joe Biden.
"I was so stinkin' embarrassed that a golf cart full of Secret Service guys had to pull up beside me. My hands just got torn up, and I was dripping blood. In the debate, you could see a big ugly Band-Aid on my right hand," Palin said.
The governor also pointed out an advantage to running: When she's out, she's just another hockey mom in running shoes.
"When I run, I'm totally incognito because I'm not wearing a trough full of makeup. I can go running through a mob of tourists and they don't recognize me," Palin said.
And for her running soundtrack, Palin said she likes to crank up classic rock n' roll, usually Van Halen and AC/DC, then keep it mellow with a little country music. She wraps up with Amy Grant songs.
The August issue with Palin's interview goes on sale July 7.