Ĉu estas okazo, en kiu unu estas pli bona uzi ol la alia aŭ ĉu ĝi estas nur via elekto? Is there occasion when one is better to use than the other or is it just your choice?
The noun firmo in the sense of an enterprise is listed in Universala vortaro and thus is Fundamenta. There is also a fundamental adjective firma, firm, stable, fast. The origin of these words is in Latin, firmus, firm, stable → firmare, to make firm, to confirm by signature. By this logic a firm, company is something that is involved in transactions which you confirm by your signature.
In order to avoid confusion, whether firmo is a simple derivation from firma or has some other meaning, one has invented the word firmao which is strickly speaking a neologism, but has replaced firmo for all practical purposes.