It is a sort of race between them. How friendly a race that is who knows. Slightly different missions but with the common goals of getting people up into space. Once Jeff gets into space for proper on a regular basis who knows what goals he'll then set himself.
Its all good at the end of the day. If nations won't compete yet on that sort of level we saw back with the early days of rockets. Its good to see private companies having a good go. Nation level space race might heat up a little more when China lands humans back on the Moon again and that will lightly threaten the USA and Russian military if nothing else. Maybe then NASA and Europe and even Russia will push a little harder. Who knows though, it might all be private from here on out.
All good though, pushing forward always.