Complex sentence: Cographs are exactly the graphs with clique-width at most 2; every distance-hereditary graph has clique-width at most 3 while the clique-width of unit interval graphs is unbounded (based on their grid structure).
Split into simpler sentences: Cographs are exactly the graphs with clique-width at most 2. However, the clique-width of unit interval graphs is unbounded (based on their grid structure).