There are a number of issues to consider with this question, and depending on the type of organisation there are usually different approaches or philosophies regarding how the information is managed.
The common scenario is to treat the public facing website and the intranet as two completely different buckets of information. This creates the least amount of dependencies (e.g. information architecture, visual design, etc.) but also the greatest potential for doubling up on cost and effort to maintain.
The opposite approach is to have an open and transparent way of presenting the same information so that the public sees what the staff sees, although this is not always appropriate to do so (e.g. if there are privacy or security risks involved with the sensitivity of the information), but it means that there is consistency in the way information is structured and presented which will result in the greatest efficiency.
In general most organisations will need to strike a balance somewhere between the two extremes. One factor you can use as an input to the decision making process is to work out what proportion of the staff within the organisation will also need (or want) to see both the public website and intranet. If it is only a small section of the staff needing to do this infrequently, then the case of creating a feature just for a small set of use cases must be weighed against the potential benefit given the time and cost required to implement such a feature.