When comparing Moai SDK vs MonoGame, the Slant community recommends MonoGame for most people. In the question“What are the best 2D game engines?” MonoGame is ranked 9th while Moai SDK is ranked 19th. 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 Fast
Because it uses Lua + C++.
Pro Gives you total control
You can use your own custom shaders and extend the language with C++. MOAI doesn't give you everything, instead it gives you the tools you need to develop any game you want.
Pro Full source code is available
So it is extendable with C++
Pro Easy-to-use particle engine
Uses a limited subset of Lua
Pro Uses Lua, with LuaJIT where possible

Pro Is used by many pro developers
Moai SDK is used by popular developers including Double Fine for their mobile game, Middle Manager of Justice, and for their Kickstarter hit, Broken Age(formerly, Double Fine Adventure.) It was also used to create the popular mobile game Bubble Ball 2.
This proves that this engine can be used to make fully-featured and fun games.

Pro API interfaces
Has options for development like Hanappe and Rapanui, providing a different way to interact with the engine.
Pro Helpful community
The Moai SDK Forum is active and users will go to great extents to answer queries, post code snippets, beta test, and even purchase and give feedback on each others' games.
Pro Helpful and detailed documentation
Although the Moai SDK is very advanced and uses complicated features, the documentation wiki thoroughly and clearly explains how to use these features, such as the Moai Cloud(a service that provides web services for your game), and multiple ways to build from source.
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.
Cons
Con Not for beginning developers
The Moai SDK has very advanced features which allow it to create powerful games. A drawback from this is that it is not very suitable for beginners.
Con Not necessarily tested or stable

Con Scarce documentation
Since it is a minimalist framework there is not that much documentation, but if you are used to reading API references and source code you are good to go!
Con Development has ceased
The last update was over a year ago. Users should not expect things to still work on future OS versions unless they're ready to fix them yourself.
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.
