US rice exports account for half of their production
<Quick back of envelope calculation>
so roughly US exported rice has ten times the market size than EU exported rice. Any idiot can face a crisis - it's day to day living that wears you out.
After a lot of dredging around, in which Eurostat was f---ing useless and the FAO not much good, I found a note from EC Trade (pdf) that contains a good summary re EU rice.
With an average yearly production of approximately 2 million tonnes out of a total world production of about 400 million tonnes and an average yearly consumption of 2 million tonnes out of global consumption of over 400 million tonnes, the EU is neither a leading world producer nor a major consumer of rice. Asia is both the leading producing area and the major consumer.
Here's the import/export balance:
Rice is imported mainly from India, Thailand, USA, and Pakistan, and exported to Turkey, Switzerland, UA Emirates, Norway... and small amounts to Mediterranean countries other than Turkey.
Rice-sector reform of the CAP has recently resulted in increased imports, reduced exports. The USDA's Rice Yearbook 2008 (pdf) gives EU 25 exports at 150,000 tons a year, with US exports at 3.3 to 3.4 million tons a year (table p. 88). So a ratio of roughly 1:23.