Quantum Key distribution is different from classical ones in that it allows Alice and Bob to detect Eve. This is because a measurement in Quantum mechanics disturbs the state. In particular for BB84, a measurement by Eve in the wrong basis destroys the correlation of Alice and Bob in the correct basis.

Unlike classical key distribution, these guarantees derive from fundamental physics laws as opposed to, say, RSA that can be broken given enough computing power/time, and so are unbreakable.

Unfortunately there can be flaws in actual implementations of the BB84 scheme, such as side-channel attacks. E91 [1] (a newer scheme) addresses these flaws and prevents these attacks.

[1] http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.67....