To be profitably exploited in medicine, nanosized systems must be endowed with biocompatibility, targeting capability, the ability to evade the immune system, and resistance to clearance. Currently, biogenic nanoparticles, such as extracellular vesicles (EVs), are intensively investigated as the platform that naturally recapitulates these highly needed characteristics. EV native targeting properties and pharmacokinetics can be further augmented by decorating the EV surface with specific target ligands as antibodies. However, to date, studies dealing with the functionalization of the EV surface with proteins have never considered the protein corona “variable”, namely the fact that extrinsic proteins may spontaneously adsorb on the EV surface, contributing to determine the surface, and in turn the biological identity of the EV. In this work, we explore and compare the two edge cases of EVs modified with the antibody Cetuximab (CTX) by chemisorption of CTX (through covalent binding via biorthogonal click-chemistry) and by formation of a physisorbed CTX corona. The results indicate that (i) no differences exist between the two formulations in terms of binding affinity imparted by molecular recognition of CTX versus its natural binding partner (epidermal growth factor receptor, EGFR), but (ii) significant differences emerge at the cellular level, where CTX-EVs prepared by click chemistry display superior binding and uptake toward target cells, very likely due to the higher robustness of the CTX anchorage.