Ambient Occlusion (AO) is a short-cut and not "real" environmental lighting. So, with your coffee cup v.s. tree example, you need to select a value that works well with a majority of the objects in your scene as compared to how your camera is placed. 

As a result, for long distance shots you'd set it for the tree; for close-ups, you'd set it for the cup.

As a rule, ambient occlusion is best used with architecture and geometrics.

Full indirect lighting is not radiosity but it does produce real AO. (Carrara doesn't actually do Radiosity - instead it does something called photon mapping which is faster) If you use a sky dome to illuminate your scene, there is no benefit to using AO. This is where you get into render settings and efficiencies. AO is good for stills and animations where there is lighting sources but possibly motion in an animation. AO will give you increased render speeds across your animation as compared to using Indirect Lighting. 

On the other hand, if you have a scene animation  where you want to light it with a sky dome but nothing in your scene moves but the camera, than saving and using an irradiance map is the way to go.