I don't think there's such thing but think of OMS as some sort of
PowerBI for the Infrastructure guys. Once you start collecting data from
servers/apps, you can pretty much build your own dashboard to display
all kinds of insights and information about the environment. While ASC
also provides insights and advisory about your infrastructure, it's
focused on security only. In fact, you need ASC configured to be able to
collect and advise on security as well within OMS. So, if its security
that you are worried about, you may be able to get away with ASC only,
if a single dashboard for advisory and monitoring around backup
operations, identity, servers, apps, security, etc. is what you need
then OMS will give you all that inclusive the build-your-own capability.
OMS is a set of services which also includes ASC. Judging by your questions by OMS you mean Log Analytics and may be Automation & Control. ASC is purely Security solution and recently (Ignite 2017) the Security and Audit solution from Log Analytics is part of ASC. ASC uses Log Analytics workspace as a platform to store the data but it is separate service. Automation & Control focuses on automation, update management and configuration management. Automation & Control uses Azure Automation and Log Analytics as platform as well. Log Analytics is for storing operational logs, searching, analyzing them and alert on them. Under the Log Analytics umbrella there are a number of different solutions that serve different needs. Thee most notable of these solutions are Service Map and Network Performance Monitor.
I hope helps. You can find more information on Microsoft docs for the services.