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The flow of funds out of U.S. equities and bonds and into Europe isn't just about the U.S. government's shutdown and debt impasse, with improvements in Europe and structural issues in the U.S. also at play.
"While we don't expect a U.S. debt default, an extension to the debt ceiling will only mean that U.S. equity markets will once again face the prospect of a readjustment of growth prospects," Jefferies said in a note.
As its growth potential deteriorates, "the U.S. is trading beyond its merits," while Europe's structural reforms are spurring a "phenomenal" turnaround, said Dr. Marie Owens Thomsen, senior economist at Credit Agricole.
Funds are clearly flowing toward Europe. In the week ended October 9, European equity funds saw inflows of $1.6 billion, marking the 15th week of net inflows, while the continent's bond and money markets saw inflows of $796 million and $5.3 billion respectively for the week, according to data from Jefferies.
But in the U.S., funds remained net sellers for the week, with money market funds shedding $27 billion, the heaviest outflow in nearly six months, while equity and bond funds saw $10 billion and $1.5 billion of net selling respectively, the data showed.
"The resilience in European equity inflows alongside a firming euro is likely to mean that European equities will outperform U.S. equities into year end," Jefferies said.
Structural issues in the U.S. may extend its underperformance. The U.S. has seen its labor-force participation rate fall to 1970s-era levels, without productivity improvements, Owens Thomsen noted, citing a recent OECD study showing the country is moving backward on education levels, with older workers much better educated than their younger peers.
(Read more: Fund managers love euro zone equities: Survey)
"There's less labor and the labor we have is less productive," she said, while adding that at the same time, companies are cash rich, but aren't bothering to invest. Less labor and less capital make for a slower growth rate and slower potential growth, she said, adding the implications for U.S. monetary policy are huge.
"Inflation will resurface faster than certain people are pricing in at the moment. In terms of monetary policy, once they start raising rates, they will have to start raising rates by more than is expected," she said, although tightening likely won't happen soon.
In addition, the U.S. political stalemate means structural reforms aren't possible, she noted. While the declining deficit is a positive, "they're cutting spending on programs where they should be spending more money," such as education, which would improve labor productivity, she said.
"It's an over-focus on the birth moment and not enough on what we're going to do with the baby," she said. She expects the deficit to begin rising again "on the other side of 2015."
(Read more: European equities looking cheap as recession eases)
By contrast, "there's no time in history where Europe has managed so much structural reform in such a short period," she said. Reforms included creating new institutions, new procedures for banks and cooperation on fiscal policy, while individual countries have seen "phenomenal" turnarounds in their fiscal conditions, with most likely to have balanced current accounts by year-end, she said.
Jefferies also sees a number of positives in Europe.
"European equities offer very high earnings per share growth for low forward multiples. U.S. earnings are forecast at just below double digits and are trading close to 15 times price-to-earnings. Equally, European equities offer double the dividend yield," it said.
"The bottom line is, there is enough good news at the margin to cause a sentiment shift in favor of Europe, particularly when U.S. revenues from overseas account for over 45% of the S&P 500," it said.
— CNBC.Com's Leslie Shaffer; Follow her on Twitter