A WPF browser project is the same as writing a java applet/application, only you use IE and .net instead. you would do it for the same reasons you would write a java application.

The main wpf cons are:

1. User must have .net installed, and use IE to access the app.
2. Slow load time (.net vm must be loaded and app jit'd)

the main wpf pros:

1. Rich UI (winforms)
2. Coding understood by windows programers

the main asp.net cons:

1. Programmer must learn web model
2. Somewhat limited UI
3. Cross browser testing required

the main asp.net pros:

1. Cross browser compatiability (universal access)