Solar 2D (formerly Corona SDK) vs ct.js

Corona SDK is completely free. That includes pro-tier plugins.

Corona SDK ships with Corona Simulator, which runs your game/app directly on your PC/Mac and updates every time you make changes.
It provides immediate feedback to your actions, you can see your changes right on the screen, without necessity to make build to device. Getting instant feedback really boosts tenfold prototyping and development speed.

It's easy to create a game that looks good on many different sized mobile devices.

With the live build feature, once you have created a build and installed on a device, you get lightning fast turnaround times because any change on the code or data is updated to the devices running the game (within the local WiFi) immediately. So changes can be tested on the real hardware within a very few seconds.
What's even more impressive, this even works flawless with multiple devices running the game. You have to use it to learn how good of a feature this is while development and even more, while doing QA. Imagine fixing bugs and everyone of your QA team/friends/whoever helps to get your game done, has all changes on his device without doing anything but waiting 5 seconds - outstanding.

Uses the great and easy-to-learn Lua programming language.

It's very quick to get things up and running with Corona SDK. The API is extensive and while it's not 100% feature-complete with the iOS API, it's close enough that you could create tons of games and never run into a roadblock.

The API docs can be found here.

Corona does not throw photoshop-like madness full of buttons editor. You can go as fast as you want, learning and building game from ground up. Eventually, you'll learn how much corona is doing for you. But to start you don't have to master complex editor software. It's a great tool to learn to start game development if you want to learn how to program and make games. Your experience will be 100% transferable to any other Pro game engine.

Corona works on OS X, Windows and Android (including Kindle Fire & Nook).

Since Corona SDK became Solar2D, it's completely free, as only some third-party plugins are paid.

Since Corona SDK became Solar2D, it's completely open source under MIT license.

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.