Comparing Battleborn to Overwatch is pointless. As a game developer, Blizzard has built a massive fan base over decades, because of that they have near limitless resources to pour into each project. While Overwatch and Battleborn have some similar aspects, they are very different games released by two very different Developers. That said, the verifiable numbers attached to Battleborn are abysmal.
The fact that player activity stabilized at around 1 k, shows that things are bleak. Sure, you can choose to look at it through percentages and compare it to Borderlands, it certainly paints a nicer picture. But your not taking into account the vast difference between Battleborn and Borderlands.
Even if no one was playing Borderlands online, you still had a massive campaign to explore. With Battleborn, if no one is around all you can do is run the same 8 missions. Battleborn NEEDS a vibrant active player base just to enjoy most of it’s features. Borderlands did not. While online activity complimented the game, it wasn’t necessary to enjoy it.
The total number of active players at any given time is too low to sustain a game that is so heavily focused on multiplayer.