The Blue origin of Amazon may be considered an older company compared to Tesla's SpaceX, but as it stands now, I think it will be very difficult to predict if Blue Origin can catch up with SpaceX. The reason is that SpaceX has been making more noise lately by intensifying efforts to ensure that it gains control of the space.
This does not mean Blue Origin has relented in its struggle to gain control of the space, but SpaceX seems to be making serious headway as it has been able to bring new things into the game. SpaceX and Blue Origin are both committed to making sure that humans and robots find the moon easily accessible, regardless of whatever their missions are.
However, while SpaceX has recorded so many failures in the past, the company has now recorded several successful orbital launches. Also, the slower-paced approach of Blue Origin shows why it may never catch up with SpaceX.