I opened a discussion in duolingo about usage of these words - they both mean "child" but they don't seem to be used in equal ways.
According to Alex, дитя is probably used mostly for a young child, while ребёнок is used for older children.
Generally people appear to be using ребёнок in singular form, as in 1 child, and дети in plural form (the stem changes a bit), as in many children.
According to user vadimfowler:
There is a number of expressions where "дитя" is used in singular: "моё дитя" is an ironic way to refer to a child, since it is a neuter gender used for a human; "чем бы дитя не тешилось..." - a common reproach to a person passionately doing something useless.
Some pretty useful real-life usage there ;)