HttpClient is the newer of the APIs and it has the benefits of
- has a good asynchronous programming model
- being worked on by Henrik F Nielson who is basically one of the inventors of HTTP, and he designed the API so it is easy for you to follow the HTTP standard, e.g. generating standards-compliant headers
- is in the .NET framework 4.5, so it has some guaranteed level of support for the forseeable future
- also has the xcopyable/portable-framework version of the library if you want to use it on other platforms – .NET 4.0, Windows Phone, etc.
If you are writing a web service which is making REST calls to other web services, you should want to be using an asynchronous programming model for all your REST calls, so that you don’t hit thread starvation. You probably also want to use the newest C# compiler which has async/await support.
Note: It isn’t more performant, AFAIK. It’s probably somewhat similarly performant if you create a fair test.