The archaeologists have been unable to discover her identity.
The archaeologists have not been able to discover her identity.
What is the difference between them?
The meaning is not significantly different between the two, and both are grammatically correct. "have been unable" suggests more finality than "have not been able", unless it is qualified with "so far" or "to date" or some similar phrase. The choice is, as Jason Bassford says, a matter of style.