Usually only a shopkeeper or someone providing a service will use “arrivederla” and it is perfectly all right to reply with “arrivederci”. The other difference is that “arrivederla” can only be used when addressing one person, whereas “arrivederci” can be used to say “goodbye” to one person or more.
What is the difference between Arrivederla and arrivederci?
Arrivederla is the most formal way to say goodbye and is best used when talking to persons in authority or to older people. Meanwhile, arrivederci is less formal—a step down from arrivederla. It's best used when the person you're talking to thinks arrivederla is too formal.
What is the meaning of Arrivederla in English?
good-bye, goodbye.