The tubing in a trombone F-attachment is going to be referred to as either having a closed wrap or an open wrap. A closed wrap, sometimes referred to as traditional wrap, trigger trombone keeps all the extra tubing confined within the bell section of the trombone as seen here:
An open wrap trigger trombone allows the tubing to go beyond the crook of the bell section as seen here:
So which is better? Most trombonists, particularly professional trombonists, say that the overall playability of an open wrap is better because the air flow through the horn is less restricted. There are simply fewer bends in an open wrap that the air must flow through than in a closed wrap. However, a closed wrap enthusiast may say that a well constructed trombone with a closed wrap can have just as good an airflow as an open wrap. Still, a closed wrap will always have more bends in the tubing than an open wrap.
There is one very good reason to have a closed wrap trigger trombone: protection from dings and scratches to the tubing or damage to the tuning slide. Because of the compactness of the closed wrap and the fact that all the tubing is confined within the bell section, it is less exposed to accidents. High school and college trombone players, especially those who will find themselves on the marching field, will probably be better off with a closed wrap trigger trombone. One can always upgrade to an open wrap on the path to professional status.