Europe and China have problems.

One has a debt crisis. The other has bubble concerns.

But where there are problems, there are often opportunities. With this in mind, I asked some of our top analysts this simple question:

Which is the bigger opportunity right now: Europe or China?

Here are their answers as well as specific companies they find intriguing.

Rick Munarriz, Fool contributor and Rule Breakers analyst
Hands down, my money's on China. The economy is growing. There is no debt crisis. The yuan and euro are passing ships in terms of valuation.

Investors can also get some ridiculous deals in the presently out-of-favor growth stocks of China. I own shares in a company called China TransInfo (Nasdaq: CTFO), a fast-growing traffic management specialist.

Analysts see China TransInfo's earnings growing 28% this year and accelerate to 45% next year. The stock is trading at 8 times this year's earnings and just 6 times next year's bottom-line target.

There are certainly some beefy risks involved in buying into a country with restrictive and anti-capitalist tendencies, but I'd sooner bet on transportation infrastructure in China than even the sexiest industries in a financially wobbly Europe.

Alex Dumortier, CFA, Fool contributor
Europe's sovereign debt crisis has received enormous coverage over the last several months; by comparison, China's bear market in stocks has gone virtually unnoticed. Both situations offer contrarian stock investors genuine opportunity right now. As of June 9, for example, the MSCI Europe index was valued at just 8.6 times trailing cash earnings, compared to 10.5 times for the MSCI US index.

However, the IMF estimates that average GDP growth for the European Union over the next five years will barely exceed 2%; the equivalent estimate for China is nearly 10% (although the latter estimate is necessarily subject to greater uncertainty). On the whole, I believe China probably offers better value than Europe right now.

Nevertheless, for non-professional investors who wish to invest in individual stocks, I would recommend ferreting around in Europe before China. Why? Europe offers higher levels of governance, higher-quality financial data, and a more favorable legal and regulatory environment, etc. -- important factors that one must consider when investing internationally.

Besides, the overwhelming pessimism concerning Europe means that some defensive European blue-chips, such as Total SA (NYSE: TOT), Novartis AG (NYSE: NVS) or Unilever (NYSE: UL) look attractively priced right now. The latter offers significant exposure to faster-growing emerging markets, too. In 2009, Unilever generated nearly 38% of its operating profits from Asia, Africa and Central and Eastern Europe, compared with just a quarter from Western Europe.

Tim Beyers, Fool contributor and Rule Breakers analyst
China is an interesting play and will be for many years, but officials there admit they can't raise the value of the yuan, as the U.S. wants, without wiping out a huge chunk of its export business. Others legitimately fear an asset bubble. In each case, it's clear that Chinese stimulus is at least partly responsible for the outsized growth we've seen in recent years.

Meanwhile, Europe's struts have crumbled under the weight of the Greek and now Spanish crisis, leading to a sharp decline in the value of the euro. As an investor, I worry about a domino effect in the region. (As in: once Spain goes, who's next?)

Even so, I'm buying Europe because the region is home to some of the world's most skilled software talent. Important businesses such as SAP have fallen a bit just for being close to these troubled economies. At some point they'll rebound and lift the fortunes of opportunistic investors when they do.

Matt Koppenheffer, Fool contributor
Whether we're talking about investing in U.S. or European companies, I don't think that we should minimize the issues facing the European economy. However, when I look at even just the U.S.-listed European stocks, there appear to be some real bargains.

Royal Dutch Shell (NYSE: RDS-A), for instance, is selling an important commodity and has a very global presence . Currently that stock is trading at 11 times trailing earnings and yielding over 6%. Telefonica (NYSE: TEF), meanwhile, is based in embattled Spain, but has a lot of exposure to fast-growing Latin America. Its trailing P/E and dividend are 9.7 and 6.8%, respectively.

But while I would definitely go after some of the opportunities in Europe, I'm a long-term investor, and success over the long term often depends on growth opportunity. For that reason, I think that if investors are going to spend their time digging into one of these two markets, China is the place to be. Given the yet-emerging nature of the economy and the very different political setup, investing in China may take more work, but I believe the results in the coming decades will prove worth the effort.

While there are undoubtedly opportunities in China-based companies -- and the team at Motley Fool Global Gains has identified some great ones -- U.S. investors can also look for U.S. companies with significant exposure to China. For KFC owner Yum! Brands (NYSE: YUM), for instance, 34% of its 2009 revenue came from China.

Those are our thoughts. Share yours in the comment area below. Or check out our roundtable on the best dividend play here.

Novartis AG and Unilever are Motley Fool Global Gains recommendations. Total A. and Unilever are Motley Fool Income Investor recommendations. Motley Fool Options has recommended a bull call spread position on Yum! Brands. Try any of our Foolish newsletters today, free for 30 days.

This roundtable article was compiled by Anand Chokkavelu, who does not own shares of any company mentioned. The Motley Fool has a disclosure policy.