We are moving a staircase to the middle of the house, and over the weekend, I opened up the basement to see if what was in the ceiling where the stairs are going.

What I found: drywall, ceiling tiles, wooden slats and another layer of drywall. By removing all layers of ceiling, I am able to get another 3 inches of head room in the basement. Basement ceiling height is low, so the 3 additional inches helps.

What are the advantages or disadvantage of removing the ceiling completely and the really old insulation, and just having open rafters in the basement ceiling?
Thanks!