No, Quantum Key Distribution is not any safer than conventional crypto is against an active Eve impersonating as Bob to Alice using the same equipment and knowledge as the rightful Bob (or/and impersonating as Alice to Bob using the same equipment and knowledge as the rightful Alice). Otherwise stated, QKD can resist
Man Eve In The Middle only inasmuch as Eve lacks some initial shared secret known only to legitimate parties Alice and Bob (or there is an independent channel with known integrity, but that's impractical).
The best QKD claims to achieve is turn an authenticated channel (or a short shared secret) into a channel safe from any eavesdropping (or an arbitrarily longer shared secret), against any attack active or passive (including by MITM). E.g. Alice and Bob start from a shared secret of say 512 bits (that could be the conventional hash of a pass phrase), assumed unknown to Eve. Alice and Bob apply some protocol with photons and mirrors, plus some elementary conventional operations on bits for post-processing; and end up with some kilo bits (per second of experiment) of random secret material unknown to Eve. Alice and Bob can use that secret material to encipher data using a One Time Pad (perhaps while they are generating that secret material, so they need not store it).
Non-quantum cryptography routinely does the same (or better: the initial trusted data needs not be secret, e.g. Alice and Bob can exchange their public key; this makes it easier to safely use asymmetric non-quantum cryptography than it is to use QKD). However non-quantum cryptography relies on assumptions on the hardness of some problem, such as the discrete logarithm problem, or/and finding more plaintext/ciphertext pairs given examples for a blockcipher; whereas QKD, and more generally Quantum Cryptography, attempts to rely only on the laws of physics.
The security track record of QKD systems is poor: one security problem has been that imperfections of single-photon sources could be exploited; another rather spectacular one was active blinding; now I'm hearing of double blinding. QKD is not practicable with the current fiber infrastructure (quantum repeaters, if any, exist in labs only). Combine with the fact that QKD solves a problem that is already solved in practice, more conveniently, by classical cryptography, and many reach the conclusion that QKD is a marvelous accomplishment but pointless in practice, except perhaps as a justification for funneling out money.
Update: the need for an initial shared secret (or a channel trusted for integrity) is acknowledged in this 2016 whitepaper by ID Quantique, a supplier of KQD equipment:
Key distillation is then complemented by an authentication step in order to prevent a “man in the middle attack”. In this case the eavesdropper would cut
the communication channels and pretend to the emitter that he is the receiver and vice versa.
Such an attack is prevented thanks to the use of a preestablished secret key in the emitter and the receiver, which is used to authenticate the communications on the classical channel. This initial secret key serves only
to authenticate the first quantum cryptography session. After each session, part of the key produced is used to replace the previous authentication key.