Motivated by the anomalous dust-to-metal ratios derived in the literature for gamma -ray burst (GRB) damped Lyman- alpha absorbers (DLAs), we measure these ratios using the dust-depletion pattern observed in UV/optical afterglow spectra associated with the interstellar medium (ISM) at the GRB host-galaxy redshifts. Our sample consists of 20 GRB absorbers and a comparison sample of 72 DLAs toward quasars (QSOs) with redshift 1.2 < z < 4.0 and down to Z = 0.002 Z# metallicities. The dust-to-metal ratio in QSO- and GRB-DLAs increases both with metallicity and metal column density, spanning ~10-110% of the Galactic value and pointing to a nonuniversal dust-to-metal ratio. The dust extinction AV increases steeply with the column density of iron in dust, N(Fe)dust, calculated from relative metal abundances, confirming that dust extinction is mostly occurring in the host galaxy ISM. Most GRB-DLAs display log N(Fe)dust > 14.7, above which several QSO-DLAs reveal molecular hydrogen, making GRB-DLAs promising candidates for molecular detection and study.