Here's a quick rundown of each area (with lots of helpful links):
Cross-platform compatibility
Ajax works in any modern browser that can run JavaScript. Flex requires Flash or anything else that can handle SWFs but, once that's installed, it's a total freeride as far as compatibility. Silverlight is tricky and misunderstood so carefully consider your userbase before going with this MS foray into the rich web applications arms race. Also keep in mind that Silverlight is still in Beta, so it may become more widely used and installed in the future as it is developed.
Performance
I'm fearful of making too many statements about performance because it really depends on how much you are willing to optimize and the exact nature of your application. Also, some technology stacks are just never going to be very fast. Some people out there have been making comparisons, but again, it depends on a great many factors (even the version of the browser from which you are testing!). It's probably best to choose based on other factors and optimize once you've started to develop.
Developer tools
There are the "golden standard" dev tools for each of the three:
Ajax has basically unlimited options, depending on the rest of your technology and architecture choices. The big questions you're actually faced with are which libraries to rely upon, and Google has voiced a pretty well adopted answer with things like Web Toolkit. When you get right down to it, it's just XML and JavaScript, right?
Flex is from Adobe and, just like with Flash development, you'd better stick with their homegrown tools because--well--they're making the standards as they go along.
Microsoft has positioned Microsoft Expression Blend versions 2.0 and 2.5 for designing the UI of Silverlight 1.0 and 2 applications respectively. Visual Studio 2008 can be used to develop and debug Silverlight applications (from Wikipedia).
Community support
There is both official and unofficial community, corporate, and open-source support for all three options. Whichever you are already integrated with and which makes you feel most at home are very individual things, but I'll offer this advice: stick with what you know. If you are a MS developer and have MSDN as your homepage, you are probably going to think the Silverlight documentation and forums are really helpful. Flex has a very similar story; the forums are pretty good and if you're a Flash person already, you're going to be right at home with their documentation and user community.
On the other hand, Ajax is basically all over the place because you can implement so many different ways and use so many widely-varied libraries. Each library can have it's own forums to visit and mailing lists to lurk within for answers.
Once again, all three have corporate giants trying to foster their communities and to get the best support possible to the developers that will give them greater market share in the future.