Moai SDK vs Gideros

Because it uses Lua + C++.

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.

So it is extendable with C++

Uses a limited subset of Lua

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.

Has options for development like Hanappe and Rapanui, providing a different way to interact with the engine.

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.

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.

Gideros provides on device players for iOS and Android that can be used to instantly try out your code directly from the Gideros IDE.

Gideros provides an easy way to target various screen sizes by providing automatic scaling options and choosing the best image resolution based on device screen automatically

You can build apps without an online dependency.

Gideros has an active forum where you can find friendly and helpful advice.

Gideros is being constantly updated and improved by the main developers.

Gideros Studio is incredibly easy to set up. Once installed it is very easy to create a new project or open one of the many example projects. Trying out an example on the desktop is two clicks away.

Gideros Studio has a very powerful feature which enables developers to use a C/C++/Java/ObjC library next to Lua. This way it's possible to call the library functions under Lua, get the results and interpret them directly under Gideros Studio.

Gideros supports iOS, Android, Windows, MacOS, WindowsRT, Windows Phone and HTML5 platforms.

2D performance is amazing.

Gideros uses the Lua programming language which is very easy to learn (and very powerful). There are some excellent video tutorials too, to help you get started. The Gideros forum community are also very friendly and helpful if you any any problems.