- SpaceX wants to enter the traditional rocket market, and use that money to slowly but surely extend into reusing rockets. This means that the most important thing is actually putting stuff into orbit, which also means that they won't do any launch that has less than a Falcon 1 capability. SpaceX has so fare managed to land 1 rocket but not reuse it.
- BO wants to enter the space tourism and do that through rocket reuse. Since there is no space tourism market yet it all has to be funded privately though. However space tourism is an entirely different beast; the requirement, for the moment, will only be to hover over the Karman line and glide back to earth safely, which is much easier than what SpaceX is doing, which means they can concentrate their efforts on other more important parts. And we've seen that in the video: they've been able to reuse a rocket, ie do what everyone is chasing, and do it successfully.
Elon Musk wants to colonize the Solar System; he's in for the very long term. BO "just" wants to send people high and get them back to earth for cheap. BO has a much more attainable goal, but they have made a bigger dent into that by reusing their first rocket.