When should I use WPF instead of DirectX? (Is DirectX dead?)

DirectX is definitely not dead and is still more appropriate than WPF for advanced developers writing hard-core "twitch games" or applications with complex 3D models
where you need maximum performance. That said, it's easy to write a naive DirectX application that performs far worse than a similar WPF application.

DirectX is a low-level interface to the graphics hardware that exposes all of the quirks of whatever GPU a particular computer has. DirectX can be thought of as assembly language in the world of graphics: You can do anything the GPU supports, but it's up to you (the application author) to support all the hardware variations. This is onerous, but such low-level hardware access enables skilled developers to make their own tradeoffs between fine-grained quality and speed. In addition, DirectX will undoubtedly expose cutting-edge features of GPUs as they emerge more quickly than they will appear in WPF.
In contrast, WPF provides a high-level abstraction that takes a description of your scene and figures out the best way to render it, given the hardware resources available. Internally, this might involve using Shader Model 3.0, or the fixed-function pipeline, or software. (Don't worry if you're not familiar with these terms, but take it as a sign that you should be using WPF!) The downside of choosing DirectX over WPF is a potentially astronomical increase in development cost. A
large part of this cost is the requirement to test your application on each driver/GPU combination you intend to support. One of the major benefits of building on top of WPF is that Microsoft has already done this testing for you! You can instead focus your testing on low-end hardware for measuring performance. The fact that WPF applications can even leverage the client GPU over Remote Desktop or in a partial-trust environment is also a compelling differentiator.