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.
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.