I'm a Macports user. Here are some things I find attractive about Homebrew:
1. While the range of packages available is only slightly larger, the support story of those packages tends to be MUCH better than Macports: a not-insignificant number of ports haven't been updated since they were first published.
2. Homebrew user docs are much better. The Macports contributor documentation is comprehensive and detailed, but their user docs are obtuse/non-existent. Homebrew contributor documentation is poor, but that lack affects a much smaller set of people than Macports' lack.
3. Homebrew is the supported install method for many pieces of open-source software: even if they also have a port, any support they give / tickets you read will be targetted to the Homebrew installation method.
The 1st and 3rd points may be mainly down to network effect but I feel like the 2nd point is very addressable and will also contribute to 1 & 3 in a big way.