Hume's conception is a more temperate one, but at the same time more vague, skeptical and relative. Neither for Hume, the substance of body or soul is not the primary focus, but the changing perceptions - becoming conscious of the bundle of perceptions characteristic for a person at a certain time. However, for Hume, these perceptions do not belong to anything; they do not belong to a "thinking substance" as with Locke. Hume holds that the "self" is utterly unobservable. In the process of introspection, all we may observe are fleeting thoughts, feelings, and experiences: never a self. Therefore, Hume's view on personal identity is not entirely clear, Locke establishes a clearer concept of personal identity, even though a contradictory one. A common point between the two philosophers is their diachronic view of personal identity. With Locke, the same soul or thinking substance is neither necessary not sufficient for personal identity over time and for Hume also, time is important in what concerns identity. However, there is also differentiation point: for Locke consciousness remains the same in the transition between thinking substances, and for Hume identity is shaped by perceptions, in the course of time. Only the large temporal frame is common, the approaches to identity in time differ.

Locke has also provided the context for the contemporary debate about personal identity by sustaining the idea of "psychological continuity" described briefly in the situation: for a to be the same person as B, it doesn't matter whether a has the same body as B (a and B. could undergo a 'body swap'), nor does it matter whether a and B. have the same soul; the only thing that matters is that B. can remember doing and experiencing all the things that a did and experienced). For Locke, memory is a facilitator of identity and a preserver of personal identity. A contemporary thinker, Intisar-Ul-Haque seems to object to by concluding...

However, for Hume, memory only acquaints us with the continuance of the stream of perceptions. However, since memory follows the stream of perceptions, a unify element should connect them, and Hume strives for unity a great deal, but only to produce the conclusion that the system - composed of the process of the fabrication of perception (impressions and ideas), imagination and memory - does not allow for a continuing, unified observer. Hence, Hume rejects the idea that memory is a necessary condition for our belief in personal identity. However, he also strives for discovering principles of association of which he identifies resemblance, spatial and temporal contiguity of impressions and ideas, and the cause-effect relation between them. However, he seems to acknowledge that memory and imagination are activated in their presence. (Preston, Aron). However, Locke also acknowledged the role of memory to revive the perceptions a person once had. It seems that both of the philosophers try to make their views specific and clear, in some points they succeed, in others they don't. They emphasize different aspects of certain mental processes and diverge in many points. At the same time, some common aspects can also be identified. The intricacy of the above issues is very high; the present essay was an attempt to establish some common points and differing views.
Works Cited

Mendus, Susan, "Personal Identity: The Two Analogies in Hume," Philosophical Quarterly, Vol. 30, No. 118 (Jan., 1980), pp. 61-68

Intisar-Ul-Haque. "The Person and Personal Identity." Philosophy and Phenomenological Research, Volume 31, Issue 1 (Sep. 1970), pp. 60-72.

Preston, Aron, David Hume's Treatment of Mind, http://www.bu.edu/wcp/Papers/Mind/MindPres.htm