We are a small indie game company. Although we've used Flash on and off since Macromedia days, we didn't fully engage Flash for mobile until Adobe announced Air Native Extensions. The main reason was the feeling of being trapped in the Flash API bubble. For example, before ANEs, the mobile market transitioned to free-to-play, In-App-Purchase, model. But because there was no way to access the native API for mobile platforms, developers on the Flash platform had to wait until Adobe releases support for it -- which may be never because Adobe, at the time, only wanted to support features that work across multiple platforms.
So, when Adobe said they will allow you to make native calls, naturally, we went nuts and embraced it. There are many ANEs out there, but I think what we do is unique, we mirror the entire native frameworks (iOS for now) and provide a higher level API for common tasks. For example, the GameKit module has hundreds of API calls and almost a hundred classes; they are all available through our GameKit ANE. It also mirrors the latest iOS version as well and we plan to keep it up to date. GameKit is an invaluable kit for anyone wanting to do multiplayer games on iOS. It supports match making, achievements, voice chat, real-time multiplayer networking and turn-based multiplayer networking all without paying for a server host and just a few API calls.
Recently, Adobe also released GameKit support for iOS through the Gaming SDK but it isn't complete. It doesn't support turn-based games for example. What we try to do is to level the playing field for Flash developers. We want everyone to be able to use all the newest native SDK features of mobile platforms as close to when they release as possible. Eventually, we will support Android, when we do, the high level API will be cross platform.