The main difference between a eukaryotic and a prokaryotic cell is the presence of a nucleus and organelles in the eukaryotic cell and their absence in the prokaryotic cell.
Amoeba contains the nucleus, as well as organelles such as vacuoles. The presence of nucleus and organelles classifies amoebas as eukaryotes.
Bacteria have neither nucleus nor organelles. Their DNA is not inside a membrane. The absence of nucleus and organelles classifies bacteria as prokaryotes.