Not undeservingly Carmack is something of a folk hero here (for example: http://h14s.p5r.org/2012/09/0x5f3759df.html) but I don't think being a 10X programmer necessarily translates into great rocket company CEO and in terms of entrepreneurial and organizational skill Bezos excels (at least based on Amazon's success).
edit: however ... I've just read that article and it is actually the most in-depth and interesting analysis I've read on the subject so thanks!
The two companies were founded in 2000. You're right about the capital, tough: as of 2014, Bezos had already invested half a billion dollars into Blue Origin.
Bezo's has more money to invest in failures and iteration than Carmack did. Also as far as intelligence goes I think they're pretty close, or Bezos would come out ahead, specifically when taking account of deep breadth of knowledge.
And motivation. Carmack's original thing was just that he was spending a lot of money on modifying Ferarris, and instead decided to put that money towards rocket development. That's not to say they took things more seriously later on, but that was the start of it.
And we learned very, very well, that H2O2 monopropellants rocket engines are a pain to use in practice, and don't seem feasible for any kind of reusable system.
In no way Armadillo Aerospace's work shown that H2O2 engines are somehow fundamentally inferior to other rocket engines. What turned AA away from H2O2 were problems to obtain rocket-grade without building a processing plant.
But I also remember lots of pictures of broken or melted catalyst on the blog. Perhaps my recollection is faulty.
You feel he could have done a better job - they both tried, Blue Origin has lasted longer and achieved more. Reality says he couldn't and didn't do a better job, so your model is inaccurate somewhere.
A quick Google suggests Carmack's net worth is ~40 million, and Bezos' ~49 billion, with over 500 million invested in Blue Origin - and experience running a successful big company. That doesn't sound like dim prospects for Bezos, does it?
This the problem with hero worship, it blinds you to the faults of your hero to the point where you're attacking others because your guy couldn't do it.