To be clear, I am not a SpaceX fanboy.
(You can feel the “but” coming)
But while a seat on crew dragon would be easily be 10 million dollars, compared to 250000 for Virgin Galactic and something similar for BO, crew dragon would be the coolest. By far.
Also, the goals of the space race agencies and modern private companies are different. Back in the days of Korelev and van Braun, NASA and the soviets were pioneers of spaceflight, almost breaking new records with each new launch. Therefore, they needed skilled and trained cosmonauts and astronauts to operate the vehicles, as they were less safe. Korelev and van Braun didn’t ride on their vehicles because they weren’t trained.
Modern CEOs have the goal of making money, so these first spaceflights were more like PR moves (though I fully support BO’s decision of inviting Wally, even if only a PR move). Branson and Bezos went on their rockets to emphasize that anyone can go to space. They also did not design the rockets that they were on.