‘Late July 2014’
The PS4 alpha kicked off recently for PlayStation 4 owners, and Xbox players were basically left in the wind. Now, based on a trailer on the Xbox One dashboard, we know that the Xbox beta will hit the platform in July. Both the 360 and Xbox One platforms were specified in the announcement.
On the PS4 side, you’ll see the beta on July 17th — so it stands to reason that “late July” for Xbox owners might be the second wave of the beta, after the PS4 has had a week or so under its belt.
Destiny beta ‘begins late July’ on Xbox systems [Joystiq]