The contributing factors were loss of outside air temperature and airspeed sensors because of icing, a dark moonless night above the ocean, and flying/falling outside of the operating range of the stall horn (when they pitched the nose down, they started recovering from the stall, airspeed went up, and the stall horn activated. when they pitched up, they went back outside of the operating range, and the horn muted).
A big contributing factor as well was that in an airbus, in normal operating conditions, pulling the stick all the way back will configure the aircraft for the best rate of climb (which can be different from just putting the elevator in full climb conditions). Due to the pitot tubes being iced up, the flight computers were in Direct mode (where movement of the sidestick is directly translated in movement of the flight controls, without computer intervention), which didn't help.
Almost that, they were in Alternate Law
The references I've seen to advantages tend to be more subtle than the AF447 tragedy. Things like the Hudson river landing where in that strange situation where you have no power the workload was diminished by having the computer keep the airplane flying most efficiently and thus be able to reach the river instead of crashing by losing airspeed.
It also makes sense the advantages are less obvious as the flight envelope protection actively prohibits dangerous situations and you can't report on non-events. The stats also show Boeing and Airbus airplanes pretty evenly matched on safety.
1: https://en.wikipedia.org/wiki/American_Airlines_Flight_587
Your perspective will influence how you classify the accidents. Proponents of full FBW will argue AF 447 happened exactly because part of the FBW system was disabled.
What's a good example in the "negotiate with the computer" camp? Perhaps it's merely a tendency on my part, but I don't think I have run across any accident which militates as strongly in favor of Airbus's design as AF 447 seems to militate against it.