Far as best practices are concerned, which is better:

public void SomeMethod(string str) 
{
    if(string.IsNullOrEmpty(str))
    {
        throw new ArgumentException("str cannot be null or empty.");
    }

    // do other stuff
}

or

public void SomeMethod(string str) 
{
    if(str == null) 
    {
        throw new ArgumentNullException("str");
    }

    if(str == string.Empty)
    {
        throw new ArgumentException("str cannot be empty.");
    }

    // do other stuff
}

The second version seems more precise, but also more cumbersome than the first. I usually go with #1, but figured I'd check if there's an argument to be made for #2.