First, Bezos and Musk are both smart, creative, and hard-working entrepreneurs.
Jeff Bezos is a bit like Captain America, calm, serious, and powerful, not allowing his emotions to prevail, he methodically moves towards his goals, Elon Musk is the real-life Iron Man, he lives in his own world and constantly innovates the world through his top inventions. He innovates things to change the future, not only working for the present, but also working on the technology of the future.
Bezos is the ultimate businessman. He makes great business decisions, Musk is a true innovator, but he also likes to talk nonsense and cause trouble, and they all have their own strengths and weaknesses.
Elon Musk has learned the ability to attract the attention of millennials and/and social media users so perfectly.
Bezos didn't get involved in that much of the high-tech industry, he ran Amazon and the space launch company Blue Origin, and many people don't know who runs Blue Origin, which is almost unknown to most people.
Musk runs Tesla, SpaceX, BoredOm, Neuralink and OpenAI. He was also the driving force behind a series of businesses that eventually became PayPal... This is as well known as Amazon, and Musk not only runs and promotes these businesses, he also does a lot of practical engineering. When he was at the Tesla factory, he actually enjoyed going to the factory floor to assemble cars because he liked it.
Bezos is a rather mysterious man who doesn't spend much time communicating with his followers on social networks, and Jeff Bezos is very respected in the tech world, but the public knows less about him, and several mentions of him have been negatively said that Amazon workers were exploited by a billionaire villain, which did not help to win public respect. That's for sure, though, in the tech world, anything Jeff Bezos says will be followed by a bunch of tech enthusiasts who are highly respected by those who really know him.
Elon Musk has always understood the incredible power of social networking. Over the years, he has become one of the most influential figures. He has nearly 50 million followers on Twitter, and he communicates in a tone close to his followers. This increases Elon Musk's popularity.
Bezos is relatively private, he doesn't do much interviewing or interacting with "mortals" through social media. Blue Origin doesn't show the world everything it does, and it doesn't go viral with every release.
Musk gives at least a few interviews a week — he chats with people on Twitter — about everything that happens at SpaceX, Tesla and TBC.
Musk smoked during the JRE (Joe Rogan Podcast). No other big business leader would dare to do that. Although Tesla's stock price fell the day after that, it quickly recovered again.
So to a certain extent, it can only be said that Musk's pro-people and geeky spirit make him more respected by ordinary people.