Microsoft’s Silverlight and Adobe’s AIR are comparable products. They compete directly. Silverlight is a complete framework. The latest versions (Silverlight 4 and AIR 2) are still in beta.
Microsoft is not as much into design. This might be changing a bit with Silverlight. It allows you to perform design and development in parallel. Silverlight uses the XAML format to describe everything. C# and therefore Silverlight are good for large projects. The .NET developers will feel at home with Silverlight.
It is hard to change your design in Adobe AIR once it is complete. A good thing about Adobe is its huge installed user base. Approximately 98% of personal computers have Adobe Flash installed now. Compare this to an optimistic 34% of PCs which have Silverlight installed.
You should go the Silverlight way if you want your app to run on both the web and the desktop. There are a lot of .NET developers out there that can move to a Silverlight development. Silverlight also makes use of the mature .NET platform. Like other environments from Microsoft, Silverlight comes with a lot of good tools.
A drawback to Silverlight is that it really has to run on the Windows platform. There is a Moonlight product that is an open source version of Silverlight. However it does not come from Microsoft. It also lags the new stuff in Silverlight by about one version. You should also probably choose Adobe if you are going to be developing mobile applications.