Differences between the space dimension

Hi all,

Trying to understand COMSOL better as I am a teaching assistant for a simulations class.

Most of the time, i know which space dimension i should be using for my model.
But for example, if i wanted measure heat transfer through an egg. I think its possible to use both 2D-axi or 3D.

but what are the difference between these dimensions? in terms of quality of the result/efficiency/ speed etc...
Any articles/papers you all can point me to would be helpful. This is a general question rather than for a specific case.

We are using COMSOL 4.3b.

Thanks