The similarity they have is that they both produce two identical cells to each other and to the mother cell, but the mechanism is totally different as binary fission takes place in prokaryotic cells while mitosis takes place in eukaryotic ones.
Primary function is reproduction. High fidelity replication in which chromosome number is maintained through a checkpoint at metaphase. Errors occur, but more rarely than in fission.
Uses cytokinesis to divide cytoplasm.