Adults are likely to notice the symbolism of the various creatures in The Neverending Story. For example, the Luckdragons can symbolize hope or a guiding force. Adults with their broader life experiences can better interpret these symbols. Also, the way the story deals with mortality in a veiled way is something adults may be more sensitive to. Kids might not fully understand the implications of the near - death experiences of the characters and what it means for the overall narrative, but adults can see it as a more profound exploration of life and death.
One thing adults will notice is the time management aspect. The way time passes differently in Fantasia compared to the real world can be related to how adults are more aware of the passage of time in their own lives. Kids may not be as attuned to this. Additionally, adults can see the social hierarchies in Fantasia more clearly. They understand how different characters are placed in the social order and what that means for the overall story, while kids might just see the characters as good or bad.
Adults might notice the economic implications in Fantasia. For example, how the different lands and their resources are managed or mismanaged. Kids are usually more focused on the adventure and the characters. Also, adults can pick up on the political undertones, like the power struggles between different factions in Fantasia which is a more complex concept for kids to grasp.