!!🚨WARNING🚨!! this post contains major spoilers for both shows, so if you haven't seen either and want to avoid major plot points I advise you to exit now.
If you haven't seen either show but still want to read this post, I explain every character and general plot mentioned so it's easy to follow along.
Before we start...
It is important to note from the beginning how grief is defined differently between Supernatural and The Haunting of Hill House. While both shows personify grief in their characters in one way or another, Supernatural’s grief is more rooted in revenge whereas The Haunting of Hill House’s grief is more rooted in fear.
This is a long post so grab some popcorn and let's get started!
Pivotal Deaths: The Haunting of Hill House
Pivotal Deaths: Supernatural
The Five Stages of Grief in both Supernatural and Hill House
Stage One: Denial
Denial:The Haunting of Hill House

Denial: Supernatural

Stage Two: Anger
Anger: The Haunting of Hill House

Anger: Supernatural

Stage Three: Bargaining
Bargaining: The Haunting of Hill House

Bargaining: Supernatural

Stage Four: Depression
Depression: The Haunting of Hill House

Depression: Supernatural

Stage Five: Acceptance
Acceptance: The Haunting of Hill House

Acceptance: Supernatural

And the Final Parallel:
An interesting parallel to both shows that plays into the idea of family is that The Haunting of Hill House ends with Hugh passing the torch of the family to Steve by saying, “This is all yours now. The house. And the promise."
Supernatural begins with John passing the family business off to Sam and Dean with Dean saying, “This is why. This book. This is Dad's single most valuable possession. Everything he knows about every evil thing is in here. And he's passed it on to us. I think he wants us to pick up where he left off, you know, saving people, hunting things — the family business."
Hill House:


So basically...
When comparing The Haunting of Hill House, a limited-series show that wraps up all its loose ends in a concise ten-episode arc, to Supernatural, a show that spans fifteen seasons despite me having only touched on Season 1, the usage of grief is vastly different; one wraps it up in a bow at the end and the other takes you through and back the stages of grief multiple times.
While the structure of The Haunting of Hill House takes the viewer through grief and defines it for them as they watch episode by episode, Supernatural brings the viewer through the bumpy reality of grief and the unhealthy or healthy ways to deal with it.