Solar 2D (formerly Corona SDK) vs BlitzMax

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.

You can compile on Windows, Mac and Linux. Nothing to change. There are solutions to compile on the same machine for 2 targets.

There are many modules to extend the features of the language: you can create PDF (via a Cairo module), or just download/upload files (via LibCurl), playing streaming sound (via BASS) and so on (databases, xml, xls...) User can create their own module (they could be written in plain BlitzMax)

Based on BASIC syntax. Supports OOP, collections (array, list and map)

After many years the language it self is very stable. The packages contains the source code of ALL modules (excluding the source of the compiler).

BlitzMax is just ready after the installation. Open the IDE, write your code and just press F5 to see the results. You don't need to install other things to use the language. Of course if you want to change the language itself - or modules - you need to install MinGW or other libs, but guidelines are provided and easy to follow.

With comparison to the some of the other languages Blitzmax compiles source files fast enough.

Good performance thanks to native code on each of the target platforms.

The language is garbage collected in two modes: reference counting or using the Boehm-Demers-Weiser conservative garbage collector.

BlitzMax provides the MaxGUI modules that allow to build GUI desktop applications for Windows, Mac and Linux (FLTK or GTK via a module). You also could create your own 'gadgets'.

the forum is plenty of examples and solutions! Community is strong and still working, available for getting an hand

BLIde is an integrated development environment for Blitz Max, designed to work very close to the project file management performed by BlitzMax engine.
It’s inspired by the .NET IDE and some other great tools, It’s been designed for hobbyist and professional coders.