The characteristics of high-power vortex Bessel beams in the terahertz range (λ=141 μm) obtained with the use of diffractive axicons (DAs) illuminated by a Gaussian beam of the Novosibirsk free-electron laser were studied. Two of the three possible types of DA recently described in our previous paper, namely, binary spiral silicon axicons (BAs), forming beams with a topological charge l equal to 0–4 and 9, and a diamond “holographic” axicon (HA), forming a beam with l=9, were used in the experiments. These axicons formed beams whose cross sections in the region of inner Bessel rings were close to those of ideal Bessel beams, but their intensities varied in azimuth with a frequency of l and 2l for the BAs and HA, respectively. However, in the case of the BAs, the beams had a pronounced helical structure at the periphery, whereas for the HA, the beam was axisymmetric. By focusing these beams with a lens, we studied the structure of the so-called “perfect” beams (PBs). While an ideal Bessel beam exhibits a PB as a thin ring, in the case of the BAs, we observed a broadened ring structure consisting of 2l short spirals, and for the HA, we observed a narrow ring with 2l maxima in azimuth. A comparison of the numerical calculations and experiments showed that the observed azimuthal intensity variations can be attributed to inaccuracies in the preparation of the axicon relief and/or discrepancies between the calculated and actual wavelengths, within a few percent. The results of this work enable the establishment of quality requirements for axicon manufacture and the appropriate selection of the axicon type in accordance with the requirements for the beam.