The paper presents results of comparative investigation of carbon nanotubes growth processes in dense low-temperature plasma and on substrate surface. Hybrid/Monte-Carlo numerical simulations were used to demonstrate the differences in the ion fluxes, growth rates and kinetics of adsorbed atoms re-distribution on substrate and nanotubes surfaces. We show that the plasma parameters significantly affect the nanotubes growth kinetics. We demonstrate that the growth rates of the nanotubes in plasma and on surface can differ by three orders, and the specific fluxes to the nanotube in the plasma can exceed the flux to surface-grown nanotube by six orders. We also show that the metal catalyst used for the nanotubes production on surface and in arc is a subject to very different conditions and this may be a key factor for the nanotube growth mode. The obtained dependencies for the ion fluxes to the nanotubes and nanotubes growth rates on the plasma parameters may be useful for selection of the production methods.