 Eukaryotes can do phagocytosis due to their cytoskeleton

Power, Sex, Suicide by Nick Lane (2006) page 53 suggests that one tremendous advantage of eukaryotes over bacteria is their ability to change shape due to the presence of the cytoskeleton, and the lack of a rigid bacterial cell wall.

Imagine in a world where there are only bacteria, and you can eat entire bacteria in one go, what a huge advantage that is!