Full disclosure - I'm the main dev behind the .NET Facebook API Client.
Now, then!
.NET Facebook API Client:
When I first released the NET Facebook API Client, the other libraries hadn't been updated in over a year. It has effectively been designed primarily with development for ASP.NET MVC in mind, though there is support for WebForms as well. While I don't generally like to toot my own horn, I've received numerous compliments that the API is very well written. It also has a generator which can automatically generate code based on Facebook's API documentation, which is very helpful for when they release new features. In general, I try to find the various pain points of working with the Facebook API and abstract over them in a way that feels natural to work with from the point of view of a .NET developer. However, this client is still in Alpha, and I haven't had as much time to devote to it as I originally had though. That said, I am still providing support via the discussion forums (and when I find questions here as well), and I also plan on another release in 2-3 weeks to add support for FQL Multiquery, an API call queueing functionality, object caching, better Facebook Connect support, as well as some other bug fixes.
Some recent love for the .NET Facebook API Client.
Facebook Developer Toolkit
Fair Warning: I haven't actually used in several years, and whatever I say here is mostly what I've read and heard from other users.
From what I understand, FDT is by far the most popular, and was probably the first .NET client written for Facebook. It was originally developed by Clarity Consulting under a contract from Microsoft (?), and has since been "supported" by the community. As I said before, when I started my client, development on this project had basically stagnated, but there has been another release since then to add support for most of the API methods added in the last 6 months or so, and from what I see on the main dev's Twitter feed, is still being actively developed. I've seen a lot of complaints about the usability and stability of this client, especially if you're wanting to use ASP.NET MVC, but I'd suggest you check out the project's discussion page and see for yourself.
Facebook.NET:
This was a great library - I had used it fairly heavily when it was being kept up to date, but it unfortunately seems to have been abandoned.