Likely the biggest difference between Silverlight 3, introduced last week, and AIR is in installation and update packaging. With Silverlight, users don't have to install anything different to get an out-of-browser and in-browser experience. With Adobe, users have to install AIR and Flash separately. The download sizes are also different. Silverlight 2 is a 4 Mbyte download, and Silverlight 3 will have a similar size. Meanwhile, Flash Player is 1.8 Mbytes and AIR a whopping 15.0 Mbytes. Silverlight apps show up as stand-alone executables, AIR apps can show up in the system registry and Add/Remove Program window in Windows. Silverlight apps are automatically updated as the developer updates them, while AIR users can have a choice of whether to update.
While AIR can read and write to a user's file system and system registry, Silverlight can do no such things. That means that on the one hand, Silverlight is at least nominally sandboxed in from doing certain types of damage to Windows -- though Adobe would and has argued against the idea that AIR isn't secure. Silverlight executables don't have access to anything outside the browser other than the ability to save new files at the user's request.
On the other hand, Silverlight lacks the many desktop hooks of AIR, like the ability to read and write from a specific file store. That means developers couldn't write a Silverlight app that allows users, for example, to do things like pull up a large folder of local images inside a Silverlight app that someone might want to choose from while posting items on eBay. That's a possible capability that isn't actually found today in eBay Desktop, an AIR application.
AIR apps also have the potential of looking more customized, since Silverlight out-of-browser apps look wrapped like any other Windows applications inside a rectangular Window. AIR apps, meanwhile, can come in any shape or size. Microsoft argues that by allowing people to erase the Window chrome, hackers could potentially hide a malicious application by making it transparent and then simply running it over top of a user's desktop.
Long story short: AIR and Silverlight compete in some ways, but don't in many others.