Long duration gamma-ray bursts (GRBs) are among the least understood astrophysical transients powering the high-energy universe. To date, various mechanisms have been proposed to explain the observed electromagnetic GRB emission. In this work, we show that, although different jet models may be equally successful in fitting the observed electromagnetic spectral energy distributions, the neutrino production strongly depends on the adopted emission and dissipation model. To this purpose, we compute the neutrino production for a benchmark high-luminosity GRB in the internal shock model, including a dissipative photosphere as well as three emission components, in the jet model invoking internal-collision-induced magnetic reconnection and turbulence (ICMART), in the case of a magnetic jet with gradual dissipation, and in a jet with dominant proton synchrotron radiation. We find that the expected neutrino fluence can vary up to three orders of magnitude in amplitude and peak at energies ranging from $10^4$ to $10^8$ GeV. For our benchmark input parameters, none of the explored GRB models is excluded by the targeted searches carried out by the IceCube and ANTARES Collaborations. However, our work highlights the potential of high-energy neutrinos of pinpointing the underlying GRB emission mechanism and the importance of relying on different jet models for unbiased stacking searches.