The .NET Framework 3.5 provides the foundation for building connected and appealing applications, productively, on a wide variety of systems from the device to the data center.

Microsoft continues to support developers using the .NET Framework platform by providing support for applications built in previous versions to the 3.5 release, so existing applications built for .NET Framework 2.0 or .NET Framework 3.0 will continue to work.

The .NET Framework 3.5 adds new features in several major technology areas:

• Deep integration of Language Integrated Query (LINQ) and data awareness.
• Support for Web 2.0 AJAX-style applications and services in ASP.NET and WCF.
• Full tooling support for WF, Windows Communication Foundation (WCF), and Windows Presentation Foundation (WPF), including the new workflow-enabled services technology.
• New classes in the base class library (BCL) for the .NET Framework 3.5 address the most common customer requests.

It's both. Ajax is a set of technologies being used together in a particular way.

Applets provide a rich experience on the client side and there are many things they can do that an AJAX application cannot do, such as custom data streaming, graphic manipulation, threading, and advanced GUIs. While DHTML with the use of AJAX has been able to push the boundaries on what you can do on the client, there are some things that it just cannot do. The reason AJAX is so popular is that it only requires functionality built into the browser (namely DHTML and AJAX capabilities). The user does not need to download and/or configure plugins. It is easy to incrementally update functionality and know that that functionality will readily available, and there are not any complicated deployment issues. That said, AJAX-based functionality does need to take browser differences into consideration. This is why we recommend using a JavaScript library such as Dojo which abstracts browser differences. So the "bottom line" is: If you are creating advanced UIs where you need more advanced features on the client where you want UI accuracy down to the pixel, to do complex computations on the client, use specialized networking techniques, and where you know that the applet plugin is available for your target audience, applets are the way to go. AJAX/DHTML works well for applications where you know the users are using the latest generation of browsers, where DHTML/AJAX "good enough" for you, and where your developers have JavaScript/DHTML/AJAX skills. Many amazing things can be done with AJAX/DHTML but there are limitations. AJAX and applets can be used together in the same UIs with AJAX providing the basic structure and applets providing more advanced functionality. The Java can communicate to JavaScript using the Live-Connect APIs. The question should not be should framed as do I use AJAX or applets, but rather which technology makes the best sense for what you are doing. AJAX and applets do not have to be mutually exclusive

XAJAX uses XML as a transport for data between the webpage and server, and you don't write your own javascript data handlers to manipulate the data received from the server. Instead you use a php class and built in javascript methods, a combination that works very similiar to the HTML_AJAX_Action class and haSerializer combo. XAJAX is designed for simplicity and ease of use.
HTML_AJAX allows for multiple transmission types for your ajax data - such as urlencoding, json, phpserialized, plain text, with others planned, and has a system you can use to write your own serializers to meet your specific needs. HTML_AJAX has a class to help generate javascript (HTML_AJAX_Helper) similiar to ruby on rail's javascript helper (although it isn't complete), and an action system similiar to XAJAX's "action pump" that allows you to avoid writing javascript data handlers if you desire.
But it also has the ability to write your own data handling routines, automatically register classes and methods using a server "proxy" script, do different types of callbacks including grabbing remote urls, choose between sync and async requests, has iframe xmlhttprequest emulation fallback capabilities for users with old browsers or disabled activeX, and is in active development with more features planned (see the Road Map for details)
HTML_AJAX has additional features such as client pooling and priority queues for more advanced users, and even a javascript utility class. Although you can use HTML_AJAX the same way you use XAJAX, the additional features make it more robust, extensible and flexible. And it is a pear package, you can use the pear installer to both install and keep it up to date.
If you're asking which is "better" - as with most php scripts it's a matter of taste and need. Do you need a quick, simple ajax solution? Or do you want something that's flexible, extensible, and looking to incorporate even more great features? It depends on the project, you as a writer, and your future plans.

As of 0.3.0, all the examples that ship with HTML_AJAX have been verified to work with
* Firefox 1.0+
* Internet Explorer 5.5+ (5.0 should work but it hasn't been tested)
Most things work with
* Safari 2+
* Opera 8.5+

Once all the major features are complete and the API has been tested, the roadmap gives an idea of whats left to be done.