We demonstrate that the conductance switching of benzo-bis(imidazole) molecules upon protonation depends on the lateral functional groups. The protonated H-substituted molecule shows a higher conductance than the neutral one (Gpro>Gneu), while the opposite (Gneu>Gpro) is observed for a molecule laterally functionalized by amino-phenyl groups. These results are demonstrated at various scale lengths : self-assembled monolayer, tiny nanodot-molecule junction and single molecules. From ab-initio theoretical calculations, we conclude that for the H-substituted molecule, the result Gpro>Gneu is correctly explained by a reduction of the LUMO-HOMO gap, while for the amino-phenyl functionnalized molecule, the result Gneu>Gpro is consistent with a shift of HOMO, which reduces the density of states at the Fermi energy.