The effect of humidity on the electrical conductivity of single-walled carbon nanotube (SWCNT) films depends on both the conductivity of individual nanotubes and the electrical contacts between them. Here, we study these factors by comparing the sensor response of nanotubes with fluorine- and nitrogen-containing groups attached to the sidewalls. Experiments carried out in a wide range of relative humidity (RH) at room and elevated temperatures showed that the conductivity of non-functionalized SWCNTs and contacts between them decreases upon the adsorption of water molecules. Covalent fluorination reduces the conductivity of SWCNTs and significantly increases the sensitivity of the film to low concentrations of water vapor. The response at high RH decreases due to the large number of water molecules adsorbed on the conductive regions of the nanotubes. As a result of substitutional reactions of fluorinated SWCNTs with dimethylformamide and ethylenediamine, nitrogen-containing groups are added, the amount of which, however, is much less than the amount of fluorine. This modification of the SWCNTs improves intertube contacts in the film and increases the surface area for water adsorption. Our results show that an increase in the number of functional groups on the SWCNT surface enhances the sensitivity of the sensor to low water concentrations and worsens the response at high RH. SWCNTs modified with ethylenediamine have the highest sensitivity over the entire range of RH.