When comparing Amethyst vs UDK, the Slant community recommends UDK for most people. In the question“What are the best 3D game engines?” UDK is ranked 17th while Amethyst is ranked 26th. The most important reason people chose UDK is:
UDK has an extremely large toolset that allows creating almost anything without having to use a 3rd party tool or plugin.
Specs
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Pros

Pro It's free and open-source
Amethyst is published under the MIT license making it open-source and id offered completely free. This allows anyone to give the tiling window manger a try, which is great.

Pro Recently updated and rewritten in Swift.
The application was written in Objective-C, but was recently updated and completely rewritten in Apple's new native language Swift.

Pro Works with keyboard shortcuts, no mouse needed
As it's designed to work closely to how xmonad, Amethyst uses keyboard shortcuts to control the windows being used, meaning no mouse input is necessary. This can make for a faster way to control windows.
Pro Multi-monitor suppport
Pro Has many common layouts to choose from (fullscreen, floating, row, column, wide, etc)
Pro Can switch between tiling and floating mode
Pro Under active development
Pro Configured via UI
No CONFIG file provides security and will avoid making amethyst crash. Instead configured via simple UI
Pro True tiling means never losing track of windows under a huge pile of others
Pro Large toolset
UDK has an extremely large toolset that allows creating almost anything without having to use a 3rd party tool or plugin.
Pro Triple A track record
UDK is an engine used by many big name companies for popular games such as the Gears of War series.
Cons
Con Can be buggy at times
Con There are more user friendly window managers available
There are certainly more user friendly window managers available for MacOS, such as Divvy or Moom. Amethyst, however, is more powerful and customizable than the more user friendly options available and therefore may be a better choice for a user looking for more advanced capabilities and customization.
Con Superseded by Unreal Engine 4
Con DevKit only runs on Windows
Even though UDK can deploy games to run on multiple platforms, including Mac, it does not feature support for development on Mac.
Con Limits games to FPS
UDK was originally developed for the FPS, "Unreal Tournament", and it certainly shows. While UDK is a very powerful engine, it takes quite a bit of work to make it do something other than an FPS.
