We present an ab initio study which identifies dominant effects leading to thermal conductivity reductions in carbon and boron-nitride nanotubes with isotope disorder. Our analysis reveals that, contrary to previous speculations, localization effects cannot be observed in the thermal conductivity measurements. Observable reduction of the thermal conductivity is mostly due to diffusive scattering. Multiple scattering induced interference effects were found to be prominent for isotope concentrations > 10%; otherwise, the thermal conduction is mainly determined by independent scattering contributions of single isotopes. We give explicit predictions of the effect of isotope disorder on nanotube thermal conductivity that can be directly compared with experiments.