Economists have reasons for measuring the way they do, it's not some evil conspiracy or something, the EU measures unemployment similarly. Labor participation rate is complicated by the retiring of the baby boomers so it's hard to use it as an indicator of labor utilization. The measure you would want to look at is BLS's U-6 which includes the normal U-3 unemployment definition and adds "Discouraged" and part time workers that would like to work more. If you look up U-6 you'll see that it's getting back down to pre-recession levels.
In any case, the point is that the US has recovered better then the EU and that is true no matter which numbers you look at.
In any case, the point is that the US has recovered better then the EU and that is true no matter which numbers you look at.