U3 is the official measurement because it has a long history and it's useful for simplifying policy decisions. It's also fairly accurate because it's largely based on unemployment insurance claims forms, which have to be re-filled every 1-2 weeks.
U6 is also an BLS measurement[1] but it not as useful. It contains far more noise and is far harder to get an accurate count (because many of the constituent groups can't be surveyed without random samples). U3 will probably continue to be used as the "official" measurement so long as there are significant tradeoffs to moving to U6.