When comparing Amethyst vs Irrlicht, the Slant community recommends Amethyst for most people. In the question“What are the best 3D game engines?” Amethyst is ranked 25th while Irrlicht is ranked 49th. 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 Lots of examples and docs
Many working examples to study and learn. You can easily experiment modifying an example code to grok in full how the engine works. In the beginning of your learning curve, the example code will offer you many useful code snippets.

Pro Free and open source

Pro Good polymorphic design
If you are considering writing your own engine with openGL, you might want to consider Irrlicht instead. It makes many features of any engine worth its salt easy, including events, serialization, nodes, animators, materials, logging, and animation. Bring your own sound and networking.

Pro Lightweight
Especially if you compile it yourself, it can be very light in memory usage.
Pro Easy to entry level C++ experience
If you want to start game developing with C++, then Irrlicht is a good candidate since it removes most of the complications in game making in C++. It will let you obtain experience in programming and games at the same time.
Pro Support for multiple formats
This engine supports multiple formats for 3D objects and textures.
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 Outdated
Obsolete over 5 years ago. While the engine is being worked on with plans for new features and support, the movement is slow, leaving many engines far more advanced in certain areas.
Con Not a game engine
This is a 3D graphics engine similar to Ogre3D. Thus, it doesn't provide any pathfinding or physics support. Support for those will have to be added by the dev.
