is a more general term used to mean 'fast'. It can also mean 'early', as in 'early in the morning' (.
specifically refers to the time taken to perform an action - an English equivalent adverb would be 'quickly', but also would mean 'deftly' or 'nimbly', and I would say in my experience implies a degree of efficiency - in your example, the girl's quick judgement of the situation.
They have slightly different applications, and although I would say they are interchangeable in this instance without sounding _too_ off, is a bit more precise.
Hope this helps!