OVz stars, a subclass of O-type dwarfs characterized by having HeII{lambda}4686 stronger in absorption than any other helium line in their blue-violet spectra, have been suggested to be on or near the zero-age main sequence (ZAMS). If their youth were confirmed, they would be key objects with which to advance our knowledge of the physical properties of massive stars in the early stages of their lives. We test the hypothesis of OVz stars being at a different (younger) evolutionary stage than are normal O-type dwarfs. We have performed the first comprehensive quantitative spectroscopic analysis of a statistically meaningful sample of OVz and OV stars in the same star-forming region, exploiting the large number of OVz stars identified by the VLT-FLAMES Tarantula Survey in the 30 Doradus region of the Large Magellanic Cloud (LMC). We obtained the stellar and wind parameters of 38 OVz stars (and a control sample of 46 OV stars) using the FASTWIND stellar atmosphere code and the IACOB-GBAT, a grid-based tool developed for automated quantitative analysis of optical spectra of O stars. In the framework of a differential study, we compared the physical and evolutionary properties of both samples, locating the stars in the logg vs. logT_eff_, logQ vs. logT_eff_, and logL/L_{sun}_ vs. logT_eff_ diagrams. We also investigated the predictions of the FASTWIND code regarding the OVz phenomenon.