Prokaryotic and eukaryotic cells differ in their structural organization. Prokaryotic cells lack membrane-bound organelles and have bacterial chromosomes not associated with histones, while eukaryotic cells have organelles like the nucleus, mitochondria and chloroplasts enclosed in membranes. Another key difference is that prokaryotic cells like bacteria are typically smaller than eukaryotic cells and lack internal compartmentalization. However, both cell types share basic chemical and metabolic similarities as living organisms.