There is slight difference in meaning between the two sentences. "What needs to be done" indicates a list of items which must be completed, but does not necessarily indicate that the bigger project will be done when those tasks are complete. "What is needed to be done", on the other hand can imply that when the list is complete, the project will be done. In effect, the first sentence says "we must do these things", and the second says "when we do these things, we will be done".
In either case, the second sentence is a bit ambiguous. I would use "what needs to be done" for the first case (when you simply have a list of tasks that must be completed). If the intent is to describe all of the outstanding tasks for a given project (the second case), I would use a more explicit sentence such as: "everything that needs to be done" or "things that must be done in order to finish this project".