I dunno. New Glenn isn't due until 2020 or so. BFR cargo will probably be flying within a few years of that, so New Glenn will be redundant a couple of years after its born. Especially as it's hard to see how Blue Origin will ever be able to reuse their second stage.
I wouldn't be surprised if BFR makes orbit before New Glenn. SpaceX have more experience with orbital-class rockets, they have a bigger company, they have the engine and fuel tank well in hand. New Glenn might be delayed. In any case, it's going to be quite close. Blue Origin may turn out to be a vanity product of a multi-billionaire, with little commercial or industrial importance.