I'd like to know what is the difference between private and public universities in Poland?
The main difference is that in public you don't have to pay, unless you study on weekends/evnings. Quality vary in both public and private.
I'd like to know how good is Wyzsza Szkola Biznesu in Nowy Sącz exactly?
It's indeed one of 3 or 4 best private business schools. I would say that It's worse than SGH and few others best public schools, but better than average economy on public university. Besides It's hard tell which is "better" - some public universities are "respected" because It's hard to pass entry exams there, but It's rather that they force people to study hard and not teach very well. I heard that the school you are asking about has a good contacts with some employers and they help to find jobs for people, who gets their degree, in public schools there is no such things.