Solar 2D (formerly Corona SDK) vs AppGameKit 2.0

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.

The AppGameKit Basic can now export to HTML5.

Supports developing games for Android, iOS, PC, Mac, Linux and now HTML5.

There is no charge for upgrades, or for extra platforms (the HTML5 version just appeared in the latest version), there are no subscription fees or other usage charges. If you publish onto either Apple or Google's stores you will have to pay their costs, of course, but the makers of AGK do not take a cut of this themselves.

Plug-ins can now be added to the Windows platform. Create your own Tier BASIC commands and call them using the AppGameKit Basic script language style.

AppGameKit supports instant testing on all connected devices. With the push of a button you can run your game on any device connected to the development machine.

Every function is fully documented with examples and exercises. The Tutorial PDF is a full Introduction to 3D game programming with integrated references to every functionality and its most important usecases. The documentation is regulary updated.

Program in tier 1 BASIC programming for every 3D game need.

A Raspberry Pi version is available and free. Users just need to register with the developer and then they can download.

It is a compilation based language, but the compilation is very fast. A project of about 1800 lines of code, for example, can compile almost instantly. (That's because it does not compile, it's an interpreter)

Informed, timely and intelligent feedback from the AGK forum.

There are plenty of functions which facilitate development and deployment. For example, the AGK player immediately plays the updated bytecode on Android devices then the online site helps with building an APK file for Google Play Store in minutes.

Software produced with the App Game Kit is written in a language called AGK Script. This language has powerful inbuild commands including commands for 2D graphics, physics and networking. The commands make use of the platforms' native functions to improve performance. They are also designed to enhance code readability. The AGK Script commands have extensive online documentation.

It runs fast with BASIC but if you want more you can use C++, it's also easy to use.

Libraries which provide the same functionality are available for the five platforms, so you can code in C++

AGK comes with an Integrated Development Environment (IDE) based on the Code::Blocks IDE for writing AGK scripts. A key feature of the IDE is its ability to broadcast compiled programs to other devices for testing.