Gideros vs Solar 2D (formerly Corona SDK)

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.

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.