I do not believe Gearbox or 2K plans on treating Xbox One players as second-class citizens (outside of the PS4 open beta and early Alani unlock because of it), but I do believe the three platforms (PlayStation 4, Xbox One, PC) will be isolated in terms of not playing with one another (correct me if I am wrong!).
Of course, Microsoft did just announce something interesting, but it remains to be seen whether Sony gets on board, especially with their dominant market position allowing them not to.
As for e-sports, I am willing to bet they will take a “wait and see” approach with respect to whether the game succeeds and builds a competitive scene before investing in it. So many games have tried to shoehorn their way into being e-sports, but most fail miserably. It seems that the ones that make it do it because the game is good and a community grows around it first, not because they host tournaments and give out prizes.