ABSTRACT We present the largest, publicly available sample of damped Ly systems (DLAs) along the lines of sight of Swift-discovered gamma-ray bursts (GRBs) in order to investigate the environmental properties of long GRB hosts in the z = 1.8-6 redshift range. Compared with the most recent quasar DLA sample (QSO-DLA), our analysis shows that GRB-DLAs probe a more metal-enriched environment at , up to . In the z = 2-3 redshift range, despite the large number of lower limits, there are hints that the two populations may be more similar (only at a 90% significance level) than at higher redshifts. Also, at high-z, the GRB-DLA average metallicity seems to decline at a lower rate than the QSO-DLAs: GRB-DLA hosts may be polluted with metals at least as far as kpc from the GRB explosion site, probably due to previous star formation episodes and/or supernova explosions. This shallow metallicity trend, now extended up to , confirms previous results that GRB hosts are star-forming and have, on average, higher metallicities than the general QSO-DLA population. Finally, our host metallicity measurements are broadly consistent with the predictions derived from the hypothesis of two channels of GRB progenitors, one of which is mildly affected by a metallicity bias, although more data are needed to constrain the models at .