Double-wall carbon nanotubes (DWCNTs) with pyridyl units covalently attached to the external wall through isoxazolino linkers and carboxylic groups that have been esterified by pentyl chains are synthesized. The properties of these modified DWCNTs are then compared with an analogous sample based on single-wall carbon nanotubes (SWCNTs). Raman spectroscopy shows the presence of characteristic radial breathing mode vibrations, confirming that the samples partly retain the integrity of the nanotubes in the case of DWCNTs, including the internal and external nanotubes. Quantification of the pyridyl content for both samples (DWCNT and SWCNT derivatives) is based on X-ray photoelectron spectroscopy and thermogravimetric profiles, showing very similar substituent load. Both pyridyl-containing nanotubes (DWCNTs and SWCNTs) form a complex with zinc porphyrin (ZnP), as evidenced by the presence of two isosbestic points in the absorption spectra of the porphyrin upon addition of the pyridyl-functionalized nanotubes. Supramolecular complexes based on pyridyl-substituted DWCNTs and SWCNTs quench the emission and the triplet excited state identically, through an energy-transfer mechanism based on pre-assembly of the ground state. Thus, the presence of the intact inner wall in DWCNTs does not influence the quenching behavior, with respect to SWCNTs, for energy-transfer quenching with excited ZnP. These results sharply contrast with previous ones referring to electron-transfer quenching, in which the double-wall morphology of the nanotubes has been shown to considerably reduce the lifetime of charge separation, owing to faster electron mobility in DWCNTs compared to SWCNTs.