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 monolayers, tiny nanodot-molecule junctions 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 the HOMO, which reduces the density of states at the Fermi energy.