To show the electron configuration for an atom when would it be better to use an orbital notation than to use a written configuration with numbers letters and subscripts

It is more convenient to use an orbital diagram when you want to show the number of unpaired electrons.

For example, the electron configuration of N is 1s² 2s²2p³.

The orbital diagram (see image below) gives the same information, but it also shows that the three 2p electrons are unpaired.

The number of unpaired electrons is useful when you are trying  to discover the magnetic properties of an atom or ion.

a:

by the combination of an unlimited number of elements