Adobe AIR is well-suited for a developer who is already familiar with Flash and AS3. It is well-suited for 2D app development using Starling or another third-party graphics library. However, to be used appropriately and avoid errors and poor performance, a basic understanding of programming principles is needed, so it's not great for a designer who hasn't studied a lot of coding.
We use it for almost all kinds of applications. It's not important if the app is small or big. It's good for DB connections, SOA architecture, office files transformations. The good thing is that it's client side, so we don't have to waste our server resources but can use the client's computer for business and visualization layer.
Although Adobe AIR is just an SDK without an actual "UI" it's commonly used within Flash, Flash Builder, or FlashDevelop. Considering the integration with Flash IDE, there are very few tools that can compete with its features.
There are definitely other platforms out there that are awesome but Adobe AIR is just what our other developers were used to using but we do have some success.
Microsoft Silverlight allows more adaptability and it integrates well with our products across the company. Adobe Flash crashes or doesn't work with our shipping campus.
Using Adobe AIR allows your team to be comprised of Flash/ActionScript 3 developers, which can be easy/cheap to find compared to other disciplines (based on location). This can lower the bottom-line in terms of engineering costs.
As the Adobe AIR SDK is free to use, the cost of entry is basically free. Additionally, the Adobe AIR SDK may be used in conjunction with a free IDE, such as FlashDevelop, making the entire stack completely free to use.
One negative impact is the stigma against Adobe Flash/AIR. Due to Adobe's less than stellar track record (in terms of support and security) with both Flash and Flash Mobile, there are numerous clients that we've dealt with, that refused to approve Adobe AIR as a tool.