Short answer: The two are identical. 
Long answer: To determine the difference between the two use Reflector (or whatever disassembler you prefer).
The code for the HttpRequest.UserHostAddress property follows:
public string UserHostAddress
{
    get
    {
        if (this._wr != null)
        {
            return this._wr.GetRemoteAddress();
        }
        return null;
    }
}
Note that it returns _wr.GetRemoteAddress(). The _wr variable is an instance of an HttpWorkerRequest object. There are different classes derived from HttpWorkerRequest and which one is used depends on whether you are using IIS 6, IIS 7 or beyond, and some other factors, but all of the ones you would be using in a web application have the same code for GetRemoteAddress(), namely:
public override string GetRemoteAddress()
{
    return this.GetServerVariable("REMOTE_ADDR");
}
As you can see, GetRemoteAddress() simply returns the server variable REMOTE_ADDR.
As far as which one to use, I'd suggest the UserHostAddress property since is doesn't rely on "magic strings."
Happy Programming