Amoeba Updated +Created
This group is a mess.
But one thing you should really know, as often mentioned in Power, Sex, Suicide by Nick Lane (2006): they are all eukaryotes.
Because prokaryotes are fundamentally unable to do phagocytosis, because they have a rigid cell wall. Changing cell shape at will requires a cytoskeleton.
Eukaryotes can do phatocytosis due to their cytoskeleton Updated +Created
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!