When comparing MonoGame vs GameApi, the Slant community recommends MonoGame for most people. In the question“What are the best 3D game engines?” MonoGame is ranked 18th while GameApi is ranked 58th. The most important reason people chose MonoGame is:
Support for iOS, Android, Mac OS X, Linux, Windows (both OpenGL and DirectX), Windows 8 Store, Windows Phone 8, PlayStation Mobile, PlayStation 4, Xbox One, Nintendo Switch, and the OUYA console with even more platforms on the way.
Specs
Ranked in these QuestionsQuestion Ranking
Pros
Pro Cross-platform
Support for iOS, Android, Mac OS X, Linux, Windows (both OpenGL and DirectX), Windows 8 Store, Windows Phone 8, PlayStation Mobile, PlayStation 4, Xbox One, Nintendo Switch, and the OUYA console with even more platforms on the way.
Pro Open source
All the code is available to you ensuring you'll have the ability to make changes when you need to or even port to whole new platforms.
Pro Well-known and documented API
The framework implements the XNA 4 API, so games made in XNA can be ported to other platforms using this. This was the same API used by the Xbox Live Indie Games platform so there's lots of documentation online for it.
Pro Managed code
By leveraging C# and other .NET languages on Microsoft and Mono platforms you can write modern, fast, and reliable game code.
Pro Good community
The community MonoGame has to offer is helpful and mature.
Pro Performance on desktop
The performance on desktop platforms matches that of C++, but you still get all the pleasant features that C# has to offer.

Pro All combinations of the features are working
In order to enable creation of 100 different kind of games, GameApi features are fully supporting all combinations of the existing features. This allows for huge amount of flexibility. The API carefully documents all dependencies between independent plugin-like modules and allows for combining their features in c++ code.

Pro Selection of 2d and 3d algorithms and techniques that construct opengl vertex arrays
The library is based on constructing opengl vertex arrays for 2d and 3d features including changing mesh colours, attaching textures, building larger worlds from smaller meshes, selection of predefined meshes like spheres, cubes and cones, Model loading from .obj files. Font support, gradient and other 2d bitmap operations, creation of 3d objects from bitmaps, Manipulation of points, lines, faces.
Cons
Con Slow rate of updates
Versions 3.9 is overdue by a year, and version 4.0 is set to release in 2040.
Con Non-Windows tools are a bit funky
Monogame support for Xamarin Studio or Monodevelop is a bit shaky especially for library references. Only good non-Windows IDE compatible with MonoGame is Rider and that costs money & isn't open-source.

Con In alpha
GameApi has just recently moved from pre-alpha to alpha status.
