Few prior efforts have been made to investigate the genetic potential of different subspecies of Triticum turgidum for drought tolerance and their quality-related traits compared with common wheat (Triticum aestivum) and to identify the association among agronomic, micronutrients, and quality-related traits, especially under climate change conditions. In this research, grain quality, technological properties of flour, and some agronomic traits were studied in 33 wheat genotypes from six different subspecies of Triticum turgidum along with three cultivars of Triticum aestivum in the field, applying a well-watering (WW) and a water stress (WS) environment during two growing seasons. A high degree of variation was observed among genotypes for all evaluated traits, demonstrating that selection for these traits would be successful. Consequences of water stress were manifested as declined DM, GY, and LASRC; and significantly increased GPC, K+/Na+, WAF, WSRC, SuSRC, and SCSRC compared to the well-watering condition. The reductions in the unextractable polymeric protein fraction and glutenin-to-gliadin ratio indicated a poorer grain yield quality, despite higher protein content. This study showed that the early-maturing genotypes had higher water absorption and pentosan, and therefore were more suitable for bread baking. In contrast, late-maturing genotypes are ideal for cookie and cracker production. Two subspecies of T. turgidum ssp. durum and T. turgidum ssp. dicoccum with high micronutrient densities and quality-related traits, and T. turgidum ssp. oriental due to having high values of grain protein content can be used to improve the quality of T. aestivum through cross-breeding programs. Based on the association of different traits with SRC values and other quality-related traits and PCA results, contrasting genotypes can be used to develop mapping populations for genome studies of grain quality and functional properties of flour in future studies.