"China is in the early stages of going from a long period where it was all about the quantity of growth, into an era where the focus is on the quality of growth," O'Neill told a news conference in Singapore.
O'Neill, who coined the term "BRICs" to describe the emerging countries of Brazil, Russia, India and China, said markets have not fully factored in the next decade of slower growth for the world's second-largest economy.
That, he said, explains the underperformance of China's stock market.
After three decades of breakneck development that saw annual growth average of 10 percent, China's government is trying to steer growth lower to complete structural economic reforms.
"We're all used to the drug of 10 percent growth and those days are behind us," said O'Neill.
As China makes its transition, O'Neill expects consumer-related and healthcare companies to benefit, while those that depend on heavy industry production and heavy industry commodities were likely to lose out.
Investors are concerned over the timing of China's planned slowdown, as it could be derailed by the global economic downturn that has sapped overseas orders for exports from China's vast factory sector.
China's CSI300 Index .CSI300 has fallen 2.2 percent so far this year, While the MSCI Asia Pacific ex-Japan's .MIAPJ0000PUS 12.5 percent rise in the same period.
O'Neill said he expected China's A-shares to rise again over the next year, and disagreed with the what he described as a growing consensus that Chinese equities would never rally again.
However, he saw China's economy continuing to struggle in the near term, and said the slowdown in growth may have spread into the July-September period, which would mark a seventh consecutive quarter of slowing growth.
"It's too soon to say a clear recovery is on the way. The Chinese economy still seems to be softening and it's possible that the economy may be weaker in Q3 than it was in Q2," O'Neill said.
"There are not many signs yet of a big easing in financial conditions, which usually is a good leading indicator of momentum."
China is not alone in facing slower growth. Goldman Sachs Asset Management expects all "BRIC" countries, except Brazil, to see lower growth than they did in the last 10 years.
However, their collective share of the world economy will still rise, and O'Neill noted that recent policy reforms that some countries like India and Brazil have introduced are a good sign.
India introduced sweeping reforms two weeks ago, such as raising the price of heavily-subsidized diesel, aimed at shoring up government finances and attracting foreign investment to revive economic growth.
(Editing by Simon Cameron-Moore)
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