Is there a LaTeX distribution for the Mac which has or comes close to MiKTeX's ability to download missing packages automatically?
MikTeX can download packages on-the-fly due to custom additions to the source code used to build compilers such as
Outside of the MikTeX distribution, I am aware of no set of TeX compilers that includes the ability to automatically download missing packages. You could try compiling and installing the MikTeX Tools which is an attempt to port the MikTeX package manager, and versions of the TeX compilers that are integrated with it, to UNIX and Linux.
Sticking with MacTeX is probably still the best way to go for a complete, stable TeX distribution on OS X. Since MacTeX is based on TeX live and not MikTeX, you won't have on-the-fly installation; but you will have the excellent
In MacTeX, TeX live is included which has tlmgr (the TeX live manager) to update and install packages (see the overview of what is included in MacTeX). There is also the TeX Live Utility, a Mac OS X graphical interface for tlmgr.