Anti vac trap or air admittance valve

What is the benefit of fitting say a 40mm or 50mm air admittance valve. As apposed to an anti vac trap at the appliance? Thanks

 

Depends on what's on the waste run, if it's just a sink then nothing else needed than an anti vac trap as you're only venting that trap using its small vent.
If there's more on the run than say 1 trapt - appliances etc, then you really want to vent the run. A 40>50mm AAV has a larger larger vent so is able to support more than one trap/outlet at a time. Even then though, supplementary venting is more applicable when there are longer runs with bends and multiple wastes feeding in, shorter lengths shouldn't really need it