Metallicity versus neutral atomic-hydrogen column density for the GRB-DLAs in our sample and the QSO-DLAs from Noterdaeme et al. (2008, 2015a; N15). Also shown are the two extremely strong QSO-DLAs from Balashev et al. (2017; B17) and Ranjan et al. (2018; B18). When molecular hydrogen is detected, the data points are colored (GRB-DLAs in red, QSO-DLAs in green and blue, as labeled). The symbol size represents the overall molecular fraction log f, and in case of a non-detection the corresponding upper limit. The GRB-DLAs at z > 4 are additionally marked with a cross. The dotted and dashed lines represent a constant metal column density of log N(X) = 12.5 and log N(X) = 13.0, respectively. Above and to the right of the scatter plot, we show the histograms and corresponding kernel density estimates for our GRB-DLAs and the N08 QSO-DLA sample. Systems with H₂ detections are colored as labeled.