The main advantage of a single booking is really that if you need to change or cancel the whole trip, with two bookings, you'll have to pay the cancellation/change fee twice. Conversely, if, say, AA cancelled one flight, on a single itinerary, both would become flexible - by contrast, on two bookings, the unaffected flight would incur the change/cancellation fee if you want to amend it even if another itinerary has been disrupted.