One advantage of closing the lid is that whatever you had open on the laptop will then “jump” to the big screen and may even figure out that there is more screen space and resize automatically. If you just open the lid and plug it in, everything you had open on the laptop remains cluttered on the small screen and your big additional desktop is just blank.

I’ve occasionally used both at once (e.g. E-mail in the small laptop window, everything else on the big screen) but that is generally for when I don’t plan to move for quite awhile. If I am constantly grabbing my machine, coming back, etc. then closed-lid is less of an interruption.