Eukaryotic cells have a nucleus surrounded by a nuclear membrane, contain organelles like mitochondria and chloroplasts, and are generally larger than prokaryotic cells. Prokaryotic cells lack a nucleus and most organelles, have only a single chromosome, and are generally unicellular. Key differences include eukaryotic cells having a nucleus with a nuclear membrane, multiple chromosomes, organelles like mitochondria and chloroplasts, and being generally larger and multicellular compared to prokaryotic cells which lack most organelles and a nucleus.