Which version should I install? Should I install Drush 8 or Drush 9 for Drupal 8?

What does the code status failing mean? Is Drush 8 not compatible with Drupal 8?
At the moment, the Drush unit tests have some intermittent failures. I wouldn't worry too much about the failure. I'd recommend Drush 8 for Drupal 8 use.

UPDATE: I looked into the test failures, and it looks like they are related to fact that Drupal 8.1.x is now the recommended version of Drupal, whereas the Drush 8 tests are still assuming 8.0.x.  These test failures have been fixed in the master branch, but not back-ported to the 8.x branch yet.  The failures are caused by problems in the tests, not by problems in Drush; they should be fixed shortly, but will not cause you any problems in the meantime.