Objectively better results at what specifically? You cannot optimize for multiple outcomes simultaneously.

The usual argument seems to be that capitalism (or the free market, or free enterprise) is the "greatest engine of wealth creation" ever. The origins of that assertion are vague. It's part of the platform of the Libertarian "Campaign for Liberty", founded in 2008:

"We believe that the free market, reviled by people who do not understand it, is the most just and humane economic system and the greatest engine of prosperity the world has ever known.

"We believe with Ludwig von Mises, Henry Hazlitt, and F.A. Hayek that central banking distorts economic decisionmaking and misleads entrepreneurs into making unsound investments."

The phrase seems to have emerged popularly during the Gingrich "Contract for America" campaign of the mid 1990s.

In the 1930s through 1950s, "engine of prosperity" was a claim attached to numerous entities or policies: railroads, advertising, debt, tariffs, etc.

In 1961, capitalism is attached to the phrase, but not in a positive light:

"was it that converted capitalism from the cataclysmic failure which it appeared to be in the 1930s into the great engine of prosperity of the postwar Western world?” In pursuit of that question, the Director of Studies at the Royal Institute of ..."

From Recent Books on International Relations - Page 998, via Google Books.

It's not until 1961 that I see the claim linked positively to capitalism or free markets, and there it's in the context of a prior political claim:

"I, too, would agree with Senator Bennett that our free enterprise economy is the greatest engine of prosperity and high living standards known"

National Alliance of Postal Employees (U.S.). - 1961, via Google Books.

Comparing per-capita GDP rankings with the Wall Street Journal / Heritage Foundation's Index of Economic Freedom, I find some correspondence, but it's at best weak.

Only half of the top 10 of each list coincide, and of the top 5, only one of the top 10 IEF nations is present (Singapore).

Six of the top-20 ranked per-capita income states come from outside the top-20 of the IEF (GDP/IEF rank): Qatar (#1/27), Norway (#4/31), Austria (#11/25), Sweden (#12/27), Iceland (#14/23), and Kuwait (#17/66). Three of these are oil states (Qatar, Norway, and Kuwait), four are highly socialized progressive states (Norway, Austria, Sweden, Iceland).

The correspondences are Singapore (#3/2), United States (#6/10), Hong Kong (#6/1), Switzerland (#7/5), Canada (#9/6), and Australia (#10/3).

Looking at the highest ranked IEF states, three of the top 10 fail to fall within the top 20 income states (IEF/GDP rank): New Zealand (#4/30), Chile (#7/54), Mauritius (#8/63).

Of the lowest IEF scores, several nations have oddly high income rankings: Argentina (#160/55), East Timor (#166/48), Iran (#168/78), Equatorial Guinea (#170/44), and Venezuela (#174/73).

Several highly respected economists have observed that economics cannot explain growth (Paul Krugman and Tony Atkinson). Most modern orthodox theories of growth date to Robert Solow's work in the 1950s, but they're strongly criticized. J.K. Galbraith associated prosperity with population and land, environmental and biophysical economists point to the associations with access to energy, though there's more than just that.

Looking at a list of nations with maximum per-capita GDP, particularly looking at the CIA's rankings (more comprehensive than the IMF or World Bank's rankings), six of the top ten nations are banking havens: Liechtenstein, Bermuda, Monaco, Jersey, Falkland Islands, and the Isle of Man. And the top-ranked nation is an oil state with a remarkably low IEF ranking: Qatar, #27 on the IEF scale. That's fewer than 50 places higher than one of the lowest per-capita GDP nations, Madagascar. Kuwait, 17th by income, is 66th on the IEF scale.

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