Adobe AIR is competing with Microsoft Silverlight in RIA domain. Adobe AIR is released a few days ago, so it is one step ahead than Silverlight 2.0.
Basically, from developer perspective, both technologies offer different paradigms. AIR is helping web developers to make desktop applications using ActionScript etc. While Silverlight is better for desktop app developers to move towards RIAs using XAML + code behind approach - the .Net 3.0 way. Web designers and developers will probably prefer AIR because of familiar development environment.
In addition, Adobe AIR SDK is available for Windows and Mac platforms. Silverlight has poor support for development on Mac - I am not aware of any decent Silverlight IDE tool is available for Mac OS yet. Putting aside the lack of OS support issue, I found that Expression Blend is quite easy to use - so designers shouldn't be worry when designing for Silverlight apps.
As for dekstop-application support, Silverlight is lacking this capability. Since Silverlight is a subset of WPF, it shouldn't be too hard to build a full blown desktop application using WPF built upon the same codebase with Silverlight (provided WPF and Silverlight 2.0 use the same XAML syntax). The only disadvantage is the .Net 3.0 deployment issue for Windows XP. Also, WPF is not a cross platform technology.
As for AIR, besides drag-and -drop, and minimize to system tray, there is not much native OS support. I have tried the AOL Music desktop application, when putting the window into dock mode, it is not docked like Windows Sidebar but placed at the desktop edge as collapsed window. I think the current OS support is enough for most of the situations.
In term of UI design, desktop applications usually are designed based on some standards, e.g. the Office 2007 ribbon UI. For web designers to design desktop applications, it is likely that they will get too creative until we have to change our behaviour in order to use the oddly designed and seriously compromised UI. Desktop AIR application, built using AJAX+HTML, may just be a web-application without web-browser window border.
For LOB applications, Silverlight gives better advantages. It is already confirmed that Silverlight 2.0 has built in data grid control. Third party component vendors are developing more Silverlight controls as well. ADO .Net team is also coming up with ADO.net Data Services (a.k.a Astoria) technology. As a subset of .Net framework, it is easier to inter-operate with WCF and WF services. So, I believe Silverlight will have more tools and resources for us to build web-based LOB applications.
Deployment isn't a big issue since both technologies are easy to deploy (approx 10mb download + a couple of seconds to install). If Siverlight 2.0 is built into Windows 7 by default, then it is even easier for Silverlight developers in the future. Another concern is the application update. .Net Framework has ClickOnce deployment technology to simplify application updating for desktop applications. I am not sure how easy it is to let the installed AIR applications auto-update themselves.
When putting Silverlight and AIR side-by-side, it is obvious Silverlight has something to catch up. Depending on the purpose of the applications, I tend to believe Silverlight will surpass Adobe AIR as the best RIA development platform in long term.