Impersonate or Assign user in Microsoft Dynamics CRM

Impersonation is someone else working on your behalf to accomplish your task. In most integration scenarios with external applications non-interactive user account is used to impersonate an interactive user. 

Non-interactive account only works when "Act on behalf" privilege is assigned. Also it will execute within the security role boundary of Interactive user. So an interactive user have access to case entity create - user or team level and on other hand non-interactive have access  at Organization level. Then only user and team level access will be granted to non-interactive. Impersonation is best where an operation shall execute in the interactive user security role context.

The above approach does not guarantee that an operation will always get complete, suppose a scenario where case-create role revoked from the interactive user, then non-interactive user acting on behalf of interactive user will not be able to perform create operation.

If the requirement is that always a case get created in dynamics CRM, then we can configure non-interactive user account and grant organization level access to create a case and assign etc, once case get created  it can be assigned to any interactive user. The difference you see here is created by user will non-interactive & owner will be interactive when you assign. On the other hand if you impersonate then created by and owner both will be interactive.