I found a nice table which will show a comparison between Microsoft products and Flash/Flex:
|Features/Benefits ||Silverlight ||.NET ||Flash/Flex|
|Rich 2D animation/graphics with audio and video ||yes ||yes ||yes|
|Industry standard video codec ||yes ||yes ||no |
|Scalable video format from HD to mobile ||yes ||yes ||no |
|Hardware-assisted editing and encoding solutions ||yes ||yes ||no |
|XML (XAML)-based presentation layer for SEO ||yes ||no ||no |
|Choice of standards-based and high-performance languages ||yes ||yes ||no |
|End-to-end server and application platform ||yes ||yes ||no |
|Media server licensing (unlimited bandwidth) ||$999 ||$999 ||$4500|
|Content access protection (DRM) ||yes ||yes ||no |
|Client side playlists for ad-insertion ||yes ||yes ||yes|
|Robust video publishing tools and third-party ecosystem ||yes ||yes ||no |
|High-performance, multi-core enabled client ||yes ||yes ||no |
|Scalable full screen video up to HD (720p) ||yes ||yes ||no |
|Native support for device-based video ||yes ||yes ||no|
|Offline, document support ||no ||yes ||no|
|Data Exchange with Web Server (Ajax, Web Service) ||yes ||yes ||yes|
|Encrypted Content ||no ||yes ||no |
|Binary or Text Format ||text 1 ||binary ||binary|
|Easy Installation Support for Platform Requirements ||yes ||no ||yes |
|Tools ||yes (Beta/CTP) ||yes ||yes |
|3D Support ||no ||yes ||no|
|3rd Party Controls ||yes 2 ||yes ||yes|
|Client size ||~2MB ||~50MB ||~2MB|
|Supported operating systems ||Windows/Mac |
1 maybe will be changed later; currently you could GZIP the content to reduce size of XAML code
2 using wpfeControl.createFromXaml(xamlstring);
3 Windows Vista and Windows XP Service Pack 2, Microsoft Internet Explorer 6, Windows Internet Explorer 7, Firefox 18.104.22.168 and 2.0.x; Apple Mac OS X, Firefox 22.214.171.124 and 2.0.x, Apple Safari 2.0.4
4 .NET 2.0: Windows 2000 Service Pack 3, Windows XP Service Pack 2, Windows Vista; .NET 3.0: Windows Vista and Windows XP Service Pack 2; Internet Explorer 6, Windows Internet Explorer 7.
5 Flash Player 8: Windows Vista and Windows XP; Internet Explorer 6 and Windows Internet Explorer 7; Windows 2000 with Internet Explorer 5.x; Firefox 1.x, Mozilla 1.x, Netscape 7.x or later, AOL 9, Opera 7.11 or later; Mac OS X, Internet Explorer 5.2, Mozilla 1.x, Firefox 1.x, Safari 1.x or later.
Will Ballard is writing in a comment about client performance. Well, this is very hard to compare because it will vary on some points. If you have a look at .NET (Click-Once or XAML Browser Application) you will have the same hardware support as installing the software directly on the client: 2D/3D graphics card, hard disk to store data and documents (compared with Cookies or Ajax server-side store),...
The performance of Silverlight and Flash will be nearly the same, I cannot see any difference. While Silverlight is using XAML as description language in a non-compressed format Flash will be faster for initial start. For Silverlight you could compress the XAML files with IIS compression enabled. There is a great Web site which simulates a Windows Vista: http://www.windowsvista.si/main.htm. I think there you can get a feeling how the performance could be.
If something is wrong or missing on this table, please leave a message and I will add it. Maybe there are other platforms missing, please give me a short hint...