What's the difference between eczema on a child's body and that of on an adult's?

As far as I know, there isn't much difference between a child's eczema and an adult's eczema, except for the one explained above. What can differ, though, is the kind of eczema--nummular eczema, hand eczema, atopic dermatitis, to name a few.

Outbreak points can differ. Usually, eczema is seen is body areas that are bendable like elbows, knees, neck, etc. Here's a reference from Google to get a clearer grasp of the outbreak points

Not much difference. It's about the same.