Nothing, they are synonymous (Response.Write is simply a shorter way to express the act of writing to the response output).
If you are curious, the implementation of HttpResponse.Write looks like this:
public void Write(string s)
{
this._writer.Write(s);
}
And the implementation of HttpResponse.Output is this:
public TextWriter Output
{
get
{
return this._writer;
}
}
So as you can see, Response.Write and Response.Output.Write are truly synonymous expressions.