Final answer:
Bacterial cells distinguish themselves from eukaryotic cells by lacking membranous organelles, such as the nucleus, mitochondria, and chloroplasts, necessary for compartmentalizing cellular processes.
Step-by-step explanation:
The property that distinguishes cells in domain Bacteria from those in domain Eukarya is the presence of membranous organelles. Bacterial cells lack these structures, which include components such as the nucleus, mitochondria, and chloroplasts. Instead, bacterial cells contain a nucleoid region where their circular DNA is located, and they may have structures such as flagella for locomotion, but all their intracellular processes occur within the cytoplasm without confinement by membrane-bound organelles. On the contrary, eukaryotic cells have a nucleus that encloses their genetic material and various membranous organelles that compartmentalize different cellular processes.