Hydrogen bonding is a central concept in chemistry and biochemistry, and so it continues to attract intense study. Here, we examine hydrogen bonding in the H2S dimer, in comparison with the well-studied water dimer, in unprecedented detail. We record a mass-selected IR spectrum of the H2S dimer in superfluid helium nanodroplets. We are able to resolve a rotational substructure in each of the three distinct bands and, based on it, assign these to vibration-rotation-tunneling transitions of a single intramolecular vibration. With the use of high-level potential and dipole-moment surfaces we compute the vibration-rotation-tunneling dynamics and far-infrared spectrum with rigorous quantum methods. Intramolecular mode Vibrational Self-Consistent-Field and Configuration-Interaction calculations provide the frequencies and intensities of the four SH-stretch modes, with a focus on the most intense, the donor bound SH mode which yields the experimentally observed bands. We show that the intermolecular modes in the H2S dimer are substantially more delocalized and more strongly mixed than in the water dimer. The less directional nature of the hydrogen bonding can be quantified in terms of weaker electrostatic and more important dispersion interactions. The present study reconciles all previous spectroscopic data, and serves as a sensitive test for the potential and dipole-moment surfaces.