Enceladus and Europa are both moons of giant planets, moving in eccentric orbits, and possessing global liquid water oceans under ice shells. Both moons exhibit tectonic features that likely formed from tidal stress due to their eccentric orbits, although additional sources of stress may have also been involved. Despite these similarities, there are several striking differences between Europa and Enceladus that we may be able to exploit to better understand the geologic processes active on each of these moons and the underlying differences in the states of their ice shells and oceans that affect geologic processes. Here, we are particularly interested in the formation of arcuate fractures called cycloids and patches of disrupted terrain called chaos features, both of which are prevalent on Europa but absent on Enceladus. Tidal stresses, due to Europa’s eccentric orbit, are thought to govern the formation of cycloids and other tectonic features on Europa. The reason only linear fractures are expressed on Enceladus’ surface is a mystery, along with why Enceladus’ tectonism is confined to certain regions and time periods while Europa’s seems to be global and consistent. Models for the formation of chaos features either invoke the presence of ocean water within the near surface of Europa or as a by-product of convection in the ice shell. Understanding why cycloids and chaos features do not form on Enceladus will aid in our understanding of the composition, thermal budget, ice shell structure, and activity on both moons and inform future exploration. We review the mechanisms for cycloids and chaos formation on Europa and identify the critical factors that must be different on Enceladus in order to inhibit formation with each mechanism. We then describe recent work on the formation of Enceladus’ fractures and constraints on its ice shell structure to look for additional clues. Finally, we discuss possible studies or future measurements that could differentiate between mechanisms as well as implications for the formation of other types of surface features.