Which party has the better record on jobs, wages?

Lucy Nicholson | Reuters

Attendees pick up leaflets at a military veterans' job fair in Carson, California.

It's still all about jobs and wages.

Despite Friday's surprisingly strong employment report — showing a gain of 271,000 new jobs last month — much of the recent presidential campaign has focused on widespread voter anxiety about their jobs and paychecks.

Even as the jobless rate has fallen to 5 percent — from double that level during the depths of the Great Recession — many Americans report a sense of uncertainty about their economic future. Despite the steady pickup in hiring over the last six years, wage growth has been sluggish, barely keeping up with inflation for most households.

So voters are listening carefully to the pronouncements from presidential candidates about which party offers the better proposals to boost job growth and wages.

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For the most part, the Republican candidates have focused on cutting regulations to free up small businesses to expand their payrolls and cutting taxes to put more money into consumer's paychecks.

"You think about the regulatory cost and the tax cost — that's why small businesses are closing, rather than being formed in our country right now," former Florida Gov. Jeb Bush said in the last GOP debate.

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Bush is right that the pace of small-business hiring — once the biggest contributor to job growth in the U.S. — has fallen across the developed world.

But it's not clear how much of the blame can be placed on government regulations. Some economists have pointed to tighter credit since the Great Recession and a relatively weak recovery that has dampened the overall appetite for risk-taking by businesses large and small.

This year, voters have more governors to choose from than at any time since the modern primary system was established in the early 1970s.

The 2016 presidential election cycle started with 10 current or former governors in the race, including former Democratic Govs. Lincoln Chafee of Rhode Island and Martin O'Malley of Maryland. The Republican field includes Govs. Chris Christie, New Jersey; John Kasich, Ohio; and Bobby Jindal, Louisiana, and former Govs. Mike Huckabee, Arkansas; Jeb Bush, Florida; Jim Gilmore, Virginia; George Pataki, New York. Wisconsin Gov. Scott Walker, and former Texas Gov. Rick Perry, who withdrew from the race after poor poll results following the initial GOP debates.

Not surprisingly, most are heavily touting successes managing their economies, including job and wage growth. But it's not clear just how much credit — or blame — voters should assign to economic policies those governors applied while in office

In the latest GOP debate, for example, Ohio governor John Kasich noted that some 347,000 new jobs have been created in the Buckeye State since he took office in January 2011. Rival Donald Trump was quick to throw cold water on Kasich's claim, made during the latest GOP debate.

"He hit oil, he got lucky with fracking," said Trump. "That is why Ohio is doing really well."

The data don't support Trump's assertion. Roughly three thousand of the jobs gained on Kasich's watch have come from the mining and logging cataloger. Job growth in Ohio has come across a wide range of industries.

Read MoreHow good are governors at creating jobs?

But Trump is correct in noting that a governor's job creation record may owe as much to national economic forces — or the policies of their predecessors — as to their own efforts once in office. Even if a governor is blessed with a legislature controlled by his or her own party, it can take years to implement a new set of "pro-job" or "pro-wage" policies.

O'Malley, for example, has pointed out that, during his term in office, Maryland had the highest median income in the nation. That's true, but Maryland also had the highest income before he took office.

On wages, Republican candidates this year are generally opposed to government efforts to raise the statutory minimum, preferring to focus on creating new jobs. As in the past, Democratic candidates generally favor government policies designed to raise incomes.

But — at the state level, at least — that's not how the two parties have governed, according to a CNBC.com analysis of some 350 governors who have served in the 50 statehouses over the last 40 years. During that period, Republican governors, as a group, generated higher wages while Democrats have created more jobs.

Of the roughly 64 million jobs created throughout the country since January 1976, more than half have been created on a Democratic governor's watch. During periods when Republicans occupied a state's governor's mansions, overall wages posted bigger total gains than the periods when Democratic governors were in office.

Still, that track record doesn't say much about what happens to governors when they get elected president.

On that score, the Democrats seem to have the better story to tell.

"Our economy and our country does better when we have a Democrat in the White House," said Democratic front-runner Hillary Clinton in her party's first debate last month. "There's a lot of evidence that when we have a Democrat in the White House, unemployment is lower, income is higher, and even the stock market is higher. But when you have a Republican in the White House you are four times more likely to have a recession."

That assertion seems to have been borne out by a paper published last year by two Princeton economists, Alan Blinder and Mark W. Watson.

The researchers looked at the data tracking U.S. gross domestic product over the last 64 years and found that the economy did substantially better when a Democrat was in office than when a Republican sat in the Oval Office — "a stunningly large partisan gap," they said.

On average, the GDP grew by 4.35 percent under Democrats and just 2.54 percent under Republicans, a gap of 1.8 percentage points. Over the 256 quarters in their sample, Republicans occupied the White House for 144 quarters and Democrats for 112. But the economy was in recession for only eight of those quarters when a Democrat was in office, compared with 49 quarters of recession under Republican administrations. That means the economy was in recession for only 1.1 quarters under Democrats and 4.6 quarters during Republican terms.

Despite the clear advantage for Democrats, the researchers were at a loss to explain why there's such a big gap in growth rates.

"Democrats would no doubt like to attribute the large D-R growth gap to macroeconomic policy choices, but the data do not support such a claim," they write.

If anything, they said, both fiscal and monetary policies seemed a bit more stabilizing when a Republican is president, "even though Federal Reserve chairmen appointed by Democrats preside over faster growth than Federal Reserve chairmen appointed by Republicans by a wide margin."

Mostly, they chalked up the difference to "good luck" on the part of Democrats.