The Silverlight plug-in means developers can target a single, consistent runtime for browser-based apps, rather than working with the complexity of multiple browsers in different versions. You also get video and multimedia effects that are hard or impossible with pure HTML and JavaScript, though Adobe Systems' Flash has the same advantages.
Over the course of months/years, various security exploits and other issues are discovered and patched in AIR, often requiring you to rebuild and resubmit mobile apps to the various storefronts. This happens often enough that it's worth mentioning as a major con.
While development on Adobe AIR seems to be fairly constant, there is very little communication between the community and Adobe regarding the future and general support of AIR. The track record of Flash (and particularly Flash Mobile) does not inspire much confidence that Adobe intends to support Flash/AIR for years to come.
Adobe AIR does not seem to perform as well (in terms of raw performance, memory usage, framerates, responsiveness, etc.) as other hybrid solutions for certain tasks. For example using shaders tends to be experimental still, and graphic/animation intensive projects often require the use of third party frameworks such as Starling.
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.
Originally, Adobe AIR was the only game in town, and its blend of flexibility in platforms it could publish to (PC, Mac, iOS, Android), ease of use, and familiarity made it the clear choice. Now Adobe no longer supports it, and we’ve found the transition to Harmon unworkable for us.
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.