The credits are no different. All deluxe credits are the same, whether they are child credits or adult credits. The GUEST pays less for the children. The restaurant is reimbursed the same amount whether it is an adult doing the ordering or a child.
However, Disney used to have the servers police who ordered what. If you were a child under 10 on the dining plan, you were supposed to order from the children's menu.
Although it has been "unofficially" released to the public that Disney will no longer require servers to do so, Disney's public literature on the dining plan does not say that. It still says children must order from the children's menu. So it's now up to the restaurant (and in some cases it may depend on your server) whether it will accept children on DXDP ordering from the adult menu.