Who is better between Leader, Coach and Manager?

Always a Leader.

People follow a leader and leaders become their inspiration. Leaders empower their team. 

Coach can only support / educate (provide guidance to) the team when they approach him

Manager can get the work done by his team reactively.

Where as leaders inspire and the team and get the work done pro-actively / voluntarily.

Leader wont demand work and there is no necessity for that, whereas, manager demands for the work to get completed.