ᐅ Single-family house with double garage, concrete vs. wooden garage roof

Hello!
We are currently building a single-family house with a double garage. During the planning stage, we had chosen a flat wooden roof for the garage.
Due to issues with the required height limits and the possible driveway clearance (I need a tall door because of a trailer), the builder has now advised us to use a concrete ceiling instead of wood.
However, this would come with an extra cost of about €2000.
Question: Is this realistic? Is a concrete ceiling really that much more expensive than wood, or is the builder trying to overcharge us?
Thank you for your responses.
Best regards, Gerd

This won’t just depend on the ceiling alone. The mass also needs to be supported in some way to prevent the trailer underneath from eventually being crushed.