We examine the properties of damped Lyman-alpha absorbers (DLAs) emerging from a single set of cosmological initial conditions in two state-of-the-art cosmological hydrodynamic simulations: SIMBA and TECHNICOLOR DAWN. The former includes star formation and black hole feedback treatments that yield a good match with low-redshift galaxy properties, while the latter uses multifrequency radiative transfer to model an inhomogeneous ultraviolet background (UVB) self-consistently and is calibrated to match the Thomson scattering optical depth, UVB amplitude, and Ly alpha forest mean transmission at z > 5. Both simulations are in reasonable agreement with the measured stellar mass and star formation rate functions at z >= 3, and both reproduce the observed neutral hydrogen cosmological mass density, Omega(HI)(z). However, the DLA abundance and metallicity distribution are sensitive to the galactic outflows' feedback and the UVB amplitude. Adopting a strong UVB and/or slow outflows underproduces the observed DLA abundance, but yields broad agreement with the observed DLA metallicity distribution. By contrast, faster outflows eject metals to larger distances, yielding more metal-rich DLAs whose observational selection may be more sensitive to dust bias. The DLA metallicity distribution in models adopting an H-2-regulated star formation recipe includes a tail extending to [M/H]