The study of oxygen chemisorption on single-walled carbon nanotubes generally relies on simple atomistic models and hence hampers the possibility to understand whether nanotube size or adduct concentration have a role in determining the surface-adsorbate interaction. Our large-scale DFT-based simulations show that structural and electronic properties as well as diffusion barriers strongly depend on both nanotube diameter and adsorbate concentration. Our atomistic models cover nanotube of different chirality with diameters from 0.6 to 1.5 nm and oxygen concentration from 0.1 to 1%. In particular, the tendency to cluster increases with concentration and stabilizes ether (ET) groups but affects hopping barriers only to a minor extent. Significant differences with graphene are found, also for 1.5 nm diameter nanotubes. Extension to species isoelectronic to oxygen reveals dissimilarities, and especially for sulfur that tends to form epoxides (EP), to diffuse more easily and to rapidly close the energy gap for increasing concentration. The relative ET-EP stability can be described in terms of the bare-bond curvature, a concentration-dependent chemical descriptor here introduced. Comparison of these DFT calculations-using different exchange-correlation functionals-and our additional investigation with a reactive force-field (ReaxFF) clarifies several similarities but also discrepancies between the predictions of the two schemes.