When comparing Amethyst vs Tombstone Engine, the Slant community recommends Amethyst for most people. In the question“What are the best 3D game engines?” Amethyst is ranked 26th while Tombstone Engine is ranked 37th. The most important reason people chose Amethyst is:
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.
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 Complete access to high quality C++ source code
Tombstone gives full access to the clean and professional C++ source code allowing editing and upgrading anything in the system.
Pro Reliable, fast and well optimized
Pro No royalties
Pro Lots of learning resources
Including extensive documentation both in code as well as online along with a wiki, tutorials and a demo game.
Pro Extending engine's functionality is straightforward
Due to the well-organized, highly modular design of the engine adding custom functionality is easy.
Pro Full-featured and modern
Comes integrated with support for physics, audio, networking, input devices, resource management as well as modern features such as real-time shadows, horizontal mapping, voxel-based terrain, dynamic lighting, post-processing effects and much, much more.
Pro Lifetime engine updates
Pro Supportive community
Tombstone has a small, tight-knit community that's well educated and professional. Eric Lengyel, the main developer, can often be found giving thorough advice to users on the forums.
Pro Proven to be a capable engine
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 Only available to big studios
Con Small community
Con Lacks D3D support
