Using the fly attached to the hammock or on separate lines is a matter of personal choice. Most of the time, I use the fly attached to the hammock. It is faster and easier to set up and take down, and requires less extra line. In fair and warm weather, the advantage of hanging the fly independently from the hammock allows for better airflow. If it is cold or in a wind-driven rain situation, keeping the fly attached to the hammock suspension allows the fly to follow the hammock more closely, making it easier to keep in warm air or keep rain out.
I guess one answer is, "It depends."
Hennessy Hammock afficionado and supporter.