I know its too longtime to reply but just as an information purpose for future readers:
WebRequest
System.Object
    System.MarshalByRefObject
        System.Net.WebRequest
The WebRequest is an abstract base class. So you actually don't use it directly. You use it through it derived classes - HttpWebRequest and FileWebRequest.
You use Create method of WebRequest to create an instance of WebRequest. GetResponseStream returns data stream.
There are also FileWebRequest and FtpWebRequest classes that inherit from WebRequest. Normally, you would use WebRequest to, well, make a request and convert the return to either HttpWebRequest, FileWebRequest or FtpWebRequest, depend on your request. Below is an example:
Example:
var _request = (HttpWebRequest)WebRequest.Create("http://stackoverflow.com");
var _response = (HttpWebResponse)_request.GetResponse();
WebClient
System.Object
        System.MarshalByRefObject
            System.ComponentModel.Component
                System.Net.WebClient
WebClient provides common operations to sending and receiving data from a resource identified by a URI. Simply, it’s a higher-level abstraction of HttpWebRequest. This ‘common operations’ is what differentiate WebClient from HttpWebRequest, as also shown in the sample below:
Example:
var _client = new WebClient();
var _stackContent = _client.DownloadString("http://stackoverflow.com");
There are also DownloadData and DownloadFile operations under WebClient instance. These common operations also simplify code of what we would normally do with HttpWebRequest. Using HttpWebRequest, we have to get the response of our request, instantiate StreamReader to read the response and finally, convert the result to whatever type we expect. With WebClient, we just simply call DownloadData, DownloadFile or DownloadString.
However, keep in mind that WebClient.DownloadString doesn’t consider the encoding of the resource you requesting. So, you would probably end up receiving weird characters if you don’t specify an encoding.
NOTE: Basically "WebClient takes few lines of code as compared to WebRequest"