The OSX support in the mainline Emacs repo (which emacsformacosx.com and aquamacs use) is a third class citizen, since very few people work on it and Stallman is always quick to remind the rest that Linux (sorry GNU/Linux) remains the priority rather than those pesky non-free OSes. The end result is that the official OSX Emacs is perpetually buggy (check emacs-devel, it breaks all the time) and lacks a lot of useful features that are available through new OSX APIs. To make matters worse, Stallman has demanded that _useful features be removed_ from the OSX branch, because _Linux doesn't have equivalent APIs_. It was disappointing to see them following through with these removals.
On the other hand, the Yamamoto Mitsuharu port is rock-solid, functionality is not removed cause Stallman said so, is actively worked on (Yamamoto was the old Carbon Emacs maintainer and knows what he's doing) and uses the latest OSX APIs. It has had flicker-free double-buffering for years, smooth (pixel-based) scrolling with inertia, integrated AppleScript bridge, integrated Apple event support, HiDPI, ligatures, graphics/SVG/animations through ImageKit, proper C-g handling, dictionary service support, proper fullscreen, and I could go on and on and on [1] ..
TL;DR
If you're using Emacs on OSX, you should be running Yamamoto's port.
[1] https://bitbucket.org/mituharu/emacs-mac/raw/892fa7b2501a403...