From my unresearched perspective, the difference is that Musk (admittedly) is pursuing crazy ventures because he's passionate about them -- and oftentimes for no other reason. He apparently originally expected that SpaceX would be broke by the time he had managed to get to Mars.
Branson seems to be deeply rooted in a business-first approach to creative innovation. "Yeah, we'll do it, but if the market accepts it."
It is unquestionable that Rb has pursued many different avenues despite there being little to no obvious commercial benefit. I do concede that you could argue it is just in the name of building his own profile, but for example did you know he started a charity aged 17, the Student advisory centre where he used to personally give advice over the phone (apparently still running) and that he started mates condoms[1] (UK based). He is also the one behind the eldars[2] (http://www.theelders.org/) and countless other projects including helping african communities establish sustainable business (to name just one).
So... brash, impulsive, and often luck-based ambition vs. careful, calculating ambition.
I'm not sure if we really need to value one over the other. The fact that Musk threw caution to the wind I do not believe is really a virtue - it just weaves a more interesting tale after the fact.
Branson seems to be deeply rooted in a business-first approach to creative innovation. "Yeah, we'll do it, but if the market accepts it."