The intricacies of web security cannot be adequately explained in a few paragraphs. Long papers have been written about just one function of web browsers in regards to security, and here Jon Donym has listed a whole bunch of functions, many of which are not directly pertinent to the larger goal of "staying secure". To explain each and every function assessed by Jon Donym would be a pointless exercise since the browser itself is only a small part of overall security and basically any up-to-date browser would have adequately secure defaults so the user would not need to change much to begin with.
What would be far more useful is a general understanding of security "best practices". The key to security, not just on the web but with anything, is to limit the things that could go wrong, to the best of our knowledge. Probably the most important aspect of security is the concept of "isolation". The basic idea is, if in the event one part of a secure chain were to fail, other parts will not fall with it. This principle can be applied to web browsing as well.
If one of your primary goals is secure online banking, the best approach would be to use a portable instance of a browser solely for online banking, or other secure transactions. I personally use a portable version of an entirely different browser located inside a Truecrypt container for email, online banking, online shopping, taxes, etc and use a portable instance of Pale Moon as my general use browser. So in the extremely unlikely event that someone were to exploit an undiscovered flaw in Pale Moon and manages to steal user data, my most important information remains secure. This is the concept of isolated browsing in action, and it is what you should do if you were truly serious about online security, instead of relying on online browser assessment tools like Jon Donym. Usually it's not your own browser that is more important but the security of the server you're connecting with, which you can assess with:
https://www.ssllabs.com/ssltest/
Another important aspect of security that's not always talked about is 'trust'. Even security professionals do not know everything there is to know about all aspects of security, online or otherwise. Before Snowden, most people thought that online security at the time was "good enough" but then we learned that many systems and protocols were too weak, and so they were deprecated. This is why there is an implicit need to trust experts in regard to their respective fields. If you can assess the security of a browser yourself, then you most likely already have. But as for me, I believe that Pale Moon comes with optimally secure defaults since I have felt little need to change anything in regards to security. If however you do not trust me or Moonchild, the developer of Pale Moon, when we say that Pale Moon is secure enough as is, then you are free to use whichever browser you trust is more secure.