Moai SDK vs ct.js

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.

ct.js is bundled with examples, docs, and easy to follow tutorials. Documentation and tutorials are available in a side panel on every screen.

You can import skeletal sprites and animations from DragonBones, which is also free. Skeletal animations are added to objects through code; developers can listen to marked events in animation, and ct.js automatically associates sounds in a DragonBones project with the game's assets.

The built-in code editor comes with error checking, type checks, code completions accompanied with docs, multiple cursors support, and other modern features.

This means that no one will ever put any features behind a paywall and that you can reliably use ct.js in any projects without worrying about licensing. And you can hack on ct.js!
The repo is at https://github.com/ct-js/ct-js

ct.js supports tiles in rooms, including collision checks and some extra editor tools, like bulk migration to a new tile layer or shifting by an exact value.

Starting with v1.0.0-next-1, you can now write WebGL games. WebGL support is based on Pixi.js.

ct.js has a "Core" library that provides basic drawing functions, room and asset management, and mouse interactions. Any other functions are added to projects as "catmods", or simply modules. These modules can be enabled or disabled in one click, and can inject their code in different game loop stages, e.g. after drawing all the objects, leaving a room, or when a new object is created.

ct.js aims to be a general game engine and provides tools in making games of any genre.

A module ct.yarn allows developers to import a YarnSpinner project to create branching, data-driven dialogues and visual novels. An example is also bundled with ct.js.
The dialogue tree is made in a separate app, though.

v1.3 brings a particle system editor, which displays a preview sprite for proper attachment of emitter to visual elements, and allows combining more than one emitter with different particles into one effect. With these, even the creation of complex, multi-step effects becomes easy. The editor comes with dozens ready-made textures for faster prototyping.