I think another common interpretation is that large diaphragm has got better bass response and small diaphragm has got better treble response.
It is usually the case in the recording industry that mics used on bass instruments are large diaphragm; in applications where good freq response for high-frequencies are needed, small diaphragms are used. e.g. pencil condensers on drum overheads (more for getting character on the cymbals than the kick).
It's not gospel, but we still see most people do it. I am still yet to see anyone use a pencil condenser on a kick drum or bass cabinet, but that of course could be due to the fragile nature of the pencils under such high SPL.