Final answer:
The false statement when comparing prokaryotes Bacteria and Archaea is that both have peptidoglycan in their cell walls. While Bacteria's cell walls are made of peptidoglycan, Archaea's cell walls do not contain peptidoglycan.
Step-by-step explanation:
The statement "Both have peptidoglycan in their cell walls" is false when comparing the prokaryotes Bacteria and Archaea. Bacteria cell walls are composed of peptidoglycan, which is made up of sugars and amino acids. In contrast, the cell walls of Archaea do not contain peptidoglycan but may be composed of other substances like pseudomurein or polysaccharides. Both groups indeed have circular DNA, lack membrane-bound organelles, and reproduce asexually through processes like binary fission.