The interface between the semiconductor and the dye is one of the fundamental parameters that directly impact the dye sensitized solar cell (DSSC) performance. In this paper the coupling between a prototype organic sensitizer and inorganic oxides is studied by a combined experimental and theoretical approach. In particular, the interface properties of the hemi-squaraine molecule (CT1) anchored onto the TiO2 and ZnO surfaces are investigated. Experimental results evidence that, beside the comparable surface coverage of the dye on both the oxides and the very fast chemisorption kinetics, TiO2 photoanodes give much larger solar cell efficiency values. Theoretical calculations based on density functional theory and time dependent density functional theory show that this difference is due to the stronger electronic coupling occurring between the CT1 anchoring group (the squaric acid) and the TiO2 surface. In this case, chemisorption induces a larger red-shift in the dye optical absorption which extends the range of harvestable frequencies if compared to the isolated dye. Moreover, the CT1/TiO2 system is characterized by an extended electron delocalization of the lowest unoccupied molecular orbital involving the substrate cations, which gives rise to easier electron injection, as confirmed by the incident photon-to-electron conversion efficiency measurements. This study demonstrates that a given dye anchoring group, although being able to form strong chemical bonds with different oxide surfaces, may be responsible for very different DSSCs performances depending on the electronic rearrangement that it undergoes upon attachment to the substrate.