I'm going to answer this under the assumption that it's a type of homework, so I'm just going to sketch the direction of each's understanding of the self rather than give a complete answer.
Aristotle's account of selfhood is largely built on his idea of substance. In the case of a human being we are a rational animal. This means that we are matter formed human-wise. Formation human-wise means that we have certain faculties such as reason (human), motion and perception (shared with other animals), ingestion, growth, and reproduction (shared with other life). Consequently, memory plays at best a minor part in our constitution.
Charles Taylor is what we might call a post-Hegelian Aristotelian. In his philosophy, he often spends a great deal of time tracing out the movement in history from one idea to another, generally due to an inadequacy in that idea (this method follows Hegel's philosophy of history in some respects). The crucial point here is that for Charles Taylor, identity is part of the story we tell about ourselves, a view often called Narrative selfhood. Consequently, memory will play an important role insofar as it's hard to have a consistent story about yourself when you have no history.