There are many RIA frameworks popping up (flex, extjs, gwt to name very few).
If my server is written in Java, why not use java web start?
The benefits I see: I get to program in a language that is easy to debug (compared to javascript), I can use the same code in server and client side (validations, model objects). With SWT I get nice looking GUI.
Even if it means requiring a plugin in the browser (or using a cli tool), if my application is an enterprise application, does it matter?
For webstart you need Java installed on the client. For Flex Flash. For Silverlight .Net. For other RIA platforms a JavaScript enabled browser. It is a lot of product politic in that question.
And Java is very intenting, because "all seems to be a nail". Of course one of the great advantages of Java: same language, same knowledge, same code on every platform or environment (server/client/middleware).
For enterprise internal use, no it does'nt matter at all. If your biz is on the internet the decison is much more complicated (or even you have to offer the same functionality in diferent platforms).