This: "In 2003, The number of people who are unemployed in Wales was two thirds the figure for England" is ungrammatical: you use "who are" which is present tense, but you're talking about the past.
The maths in the rest of it is confusing. Wales is a much smaller country than England, and so you wouldn't normally compare numbers of unemployed people, as that gives the wrong impression. You would instead compare percentages, as you do in the second example.
However, in the second example, it's still confusing because the maths is ambiguous or confusing. "two thirds above that" sounds like you're asking people to work it out for themselves: like saying "Take the English percentage. Work out what two thirds of that is, and then add it on." Cue the reader going "ok, hang on, you haven't actually told me what the English percentage is."
Since you're talking about percentages, name the percentages. You could say
"In 2003, unemployment in England was at 25 percent, compared to just 15 percent in Wales. In other words, unemployment in England was two-thirds higher than that in Wales."