Eubacteria and archaebacteria have a wide variety of shapes. However, these cell types have no membrane-bound organelles, they do not organize their DNA into a nucleus, and they are contained by cell membranes protected by cell walls. Both are relatively simple in structure, so most of their differences are chemical, not structural. In general, archaebacteria have commonalities with eukaryotes that eubacteria lack, but they also have some truly unique features.
Compared to archaebacteria, eubacteria are extremely diverse and widespread, but they have only three major cell shapes. They are either spherical, shaped like short rods, or long and twisting. This basic shape is a large part of how eubacteria are classified. Archaebacteria, on the other hand, are not classified by shape, but by the type of extremophile they are. Archaebacteria live in hostile environments that neither eubacteria nor eukaryotes can survive. They are classified as either methane producers, extreme heat specialists, or extreme salinity specialists.
Part of what makes archaebacterial survive in such extreme environments is their unique cell membranes. While all eubacteria and eukaryotes have phospholipid bilayers as their cell membranes, archaebacteria have branched hydrocarbon chains with ether links to glycerol for their membranes. This unique membrane type is more stable than those in other forms of life, and allows them to withstand extreme conditions.