I have mostly done GUI development using Java Swing. But I have also used some JavaScript and jQuery for web applications.
The things that have been much easier with JavaScript web applications are:
This makes deployment much easier. The user doesn't have to install anything, and the application silently upgrades on the next request (if a new version is available). This also makes server development easier since it's mostly not more than one client version that is used.
Built-in network client
It helps a lot that the web browsers handle all network connections for you. In example when you want to post messages to the server, you have to do almost nothing to handle the network connection. Compare this to using Apache HTTP Client, specially when you want to use a secure connection via HTTPS. The new Websockets will make this even more powerful.
Easier to make layout
This may only be an advantage against Java Swing, but maybe not compared to WPF. But doing the layout declaratively using HTML+CSS helps a lot compared to as in Java Swing where all layout is done using Java code. That would be like making layout and use of components only via JavaScript.
Easier to make asynchronous programming
Consider a sign-up form, where the user chooses a "username" and fills other fields with information. In JavaScript it's very easy to asynchronously check (using Ajax) if the username is already in use without blocking the UI, while the user can continue to fill in the other fields - and if the username is already in use, notify the user about it. In many other native GUI frameworks, you have to fire up a new thread for such asynchronous things and make the code less readable as in JavaScript+Ajax.