Two key things to note:

1. The itil role is meant for standard help desk use: Open Incidents[Problem, Change], Close Incidents [Problem, Change], Update Incidents [Problem, Change].

2. The itil-admin role provides additional functionality which is useful for governance purposes. It provides the ability for a team leader to delete Incidents [Problem, Change].  This is useful if for example duplicates have been inadvertently created. 

Note Further: A really important feature of the itil_admin role is that it is the equivalent of the sn_cmdb_admin role.  This means that the itil_admin role has full access to the CMDB [cmdb data, tools and user interfaces].