"But everytime I have looked at the data, the US is not the leader in yield"
But then yield isn't the only measure of productivity. Yield is output per acre. Where land is plentiful, like the US, there is less pressure to increase yield. In Europe, where land is less plentiful, yields are high.
On the other hand, output per labourer is high in the US. Between 1948 and 1994 farm output increased 2.37 times, but labour input reduced by two thirds. (Agricultural Productivity in the United States. By Mary Ahearn et al U.S. Department of Agriculture. Information Bulletin No. 740, p 5 http://www.ers.usda.gov/publications/aib740/aib740.pdf )
Application of fertilisers and pesticides sets Americans free to do other things, while less developed nations have a greater proportion of people tied to the land. It all depends on what you think is important. If people are important, then increased productivity is a better thing that increased yield. (In any event, new techniques in agriculture are also increasing yield, leading to more land being freed from agricultural use.)
ALSO, increased productivity makes food cheaper. In 1995, Britons spend 14 per cent of their income on food, Americans ten per cent.