Amumu needs more movement speed, he is more of a damage tank than a utility tank like a malphite. His kit requires him to be closer to people to really reach his full potential, and his only dash is a skillshot.
I often find myself build boots of swiftness, which is really not ideal on a tank. He jsut has no way to be sticky to targets, and because of it his damage is often times mitigated jsut from people outrunning all of his damage.
Amumu plays alot like singed, but singed is a very sticky champ that excels in chases.