They both work well (we can and do quibble about the internal mechanics of each), and appeal to different groups of people.
My theory is that Homebrew was announced at exactly the right time in the MacOS adoption curve. A huge number of new users arrived with no existing knowledge of MacPorts or Fink. Most of them didn't know they needed a package manager at first, but when the momentum picked up, Homebrew was the new option with a better web page, a more collaborative working model, and hosted at GitHub (also ascendant).
I'd also argue that similar factors were involved in Linux's popularity over BSD in the 1990s.
Timing, environment, adequacy, and luck. All are required. Superiority is not.