Let's do it the other way: I've used MacPorts since 2006 without a single issue, what problems will I be able to fix by switching to Homebrew?

I remember when I upgraded to Lion everything got messed up. I had to spend a whole day mucking about trying to fix thing. I remember the only solution was to get a list of everything installed, uninstall everything, reinstall the latest version of MacPorts and then reinstall all the original packages.

Migration is still required to reinstall ports as the underlying system libraries change on a major version upgrade of Mac OS X.

However, situation still improved a lot since then. If the licensing of the port and all dependencies allow it, MacPorts now even offers pre-compiled binary archives for Snow Leopard, Lion and Mountain Lion. Often you do not even have to compile software yourself anymore.

I use macports because it has better support for multiple version of python installed in parallel.