Both Flash and Air use the same AS3 code to run, and Air is fully supported across mobile devices and is well known among developers. This makes AS3 a great language to develop for projects releasing on mobile and web platforms, including FaceBook.
I have been working with Adobe Flash since the release of Macromedia Flash 4 in 1999, and am still very happy with it. Flash allows artists and programmers to work together, with simple timeline animations and extensive art tools, making it very appealing to work with on many different projects. You even don’t need to be delivering a Flash product to take advantage of it as a production tool. Using CreateJS to make a HTML5 game, for example, can take it’s animations and graphics exported straight from flash, and they look amazing.
One of my favourite things about Flash is how it maintains a consistent look and feel across a large number of supported devices. Flash does this in the same way that Java or Unity does it, and that is with a Flash player application that runs a virtual machine that renders the content, and thus is able to be consistent even with new hardware configurations. Fonts have some issues here, but that’s due to how the operating system is handling the font in question, but there are built in solutions for this as well.
Flash is made to be run inside of a web browser, and with as few other Flash items running at the same time as possible. Game portals, like FaceBook, are perfect for this. Flash uses the Action Script 2 ( AS2 ), or ( AS3 ), languages, however I would only ever recommend AS3. You also do not need the Adobe Flash Application installed to make Flash content, you can make the content directly from an AS3 source project.
Air is very similar to Flash, but instead of being targeted for a web browser, it’s target is to be run directly on the operating system, including: Windows, OSX, iOS, Android and other. Air is also compiled directly from an AS3 source project.
Air is a great solution for publishing to mobile devices, especially on a project that will also wish to publish on the web or as a downloadable air application. All of those publish targets would be made from the exact same AS3 source project, which means there is no need to port the game to these platforms, saving the client time and money.