On a Resources per capita metric the world's richest REE country is by far and away Greenland with 4,890 contained tons for a population of around 66,000 people.
Australia is the world's second richest country and hosts both the world's richest Rare Earth deposit at Mt Weld, W.A. and the richest heavy Rare Earth deposit at Dubbo, NSW.
http://www.australianrareearths.com/Known-REEs-resources-reserves
Of note Australian companies own both the Greenland deposit and those within Australia.
In two recent studies the USGS and European Union studies of mineral supply risk, REE rank highest as mineral raw materials of critical concern, given uncertain future supplies and their importance to advanced industrial economies.