The adsorption of aromatic molecules onmetal surfaces leads to a complex reorganization of the molecular and metal wave functions. Various processes such as charge transfer, hybridization between molecular and metallic states, and the formation of dispersing bands within the interface have been demonstrated for organometallic interface systems. For the model molecule 1,4,5,8-naphthalenetetracarboxylic dianhydride (NTCDA), we compare highly ordered monolayers on Ag(110) and Cu(100), which allows us to identify changes of the interfacial electronic structure when altering the coupling strength with the substrate by means of angle-resolved photoelectron spectroscopy. The stronger coupling to the Ag(110) substrate goes along with a shorter photohole lifetime and a stronger hybridization of the NTCDA lowest unoccupied molecular orbital with metal states. Supported by ab initio calculations, we show that the observed band dispersion is greatly enhanced due to the interaction with Ag(110) while the laterally denser adsorption geometry of NTCDA on Cu(100) entails a larger intermolecular wave-function overlap, and the presence of the substrate results in no further bandwidth enhancement.