Both bacteria and archaea have distinct ribosomal RNAs (rRNAs). Archea has three RNA polymerases, like eukaryotes, but bacteria only one. Archaea have cell walls that lack peptidoglycan and have membranes that encapsulate lipids with lipids rather than fatty acids (not bilayers). These lipids in archaeal membranes are unique and contain ether rather than ester bonds between glycerol backbones. Archaea are more like fungi than fungi. Their ribosomes are more like eukaryotic ribosomes than bacterial ribosomes.
The two microbes also differ genetically and biochemically. Only in the last few decades have archaea been recognized as a distinct area of life. They are extremophiles, meaning they thrive in physical or geochemical extremes. They have a similar ecological role to bacteria. Both organisms respond to various antibiotics in different ways.
Archaea: cell membranes contain ether bonds; cell walls lack peptidoglycan; genes and enzymes behave more like eukaryotes; have three RNA polymerases, like eukaryotes; and extremophiles
Bacteria: Cell membrane contains ester bonds; cell wall is composed of peptidoglycan; has only one RNA polymerase; responds to antibiotics in a different way than archea.