Well, there is no parenting across comps. Depending on exactly which properties you need to control, you might be able to do it with expressions, but implementing a full-blown expression-based parent simulation would be pretty challenging.
Here’s one example. With parenting, you attach the child to the parent. If you move the parent, the child moves. If you try to simulate that with an expression, when you move the parent, the expression has no idea where the parent used to be (unless the move is keyframed) so it doesn’t know what to do. So you can’t do the static positioning that you can do with parenting. I gets complicated in a hurry.
Dan