The difference is usually interpreted thus. The word some is normally used in neutral sentences, whereas any is often used in negative sentences. This becomes clear in the following examples:
She gave him any more soup. [any not expected in a basic statement]
She didn't give him any more soup. [any expected in a negative statement]
She gave him some more soup. [some expected in a positive statement]
?She didn't give him some more soup. [some not expected in a positive statement; this only works in special circumstances, like echo statements or contrastive focus:]
I hear she gave him some more soup. — Ah, but she didn't give him some more soup: she practically forced the entire pan down his throat!
In a question, any is often connected with a negative expectation: an answer like "no" seems likely or at least very well possible to the asker.
So in this case you're indicating to your customers by any that you probably don't expect them to want more soup—or at least you expect this less than if you had used the neutral some. Since it is a waiter's job to seem welcoming and generous (with paid consumptions, but still), when he uses some, he indicates that he will not at all be surprised if you say "yes".
Simplified, this is taught in many schools as follows: a question with some expects "yes" or "no", while a question containing any expects "no".