A shared shuttle means there are other passengers going to other locations in Paris. Typically the company arranges that you are traveling in the same area as others.
Private is just that - private only your group is in the shuttle - straight point A to B.
Sometimes the pros to a shuttle is the cost per person. There are no additional fees typically for baggage unless you are traveling with many trunks for example. Taxis will charge for bags. With a shuttle reservation - your transport is waiting for you - rather than you waiting in a line for the taxis. Shuttle service is usually available around the clock - if there is a strike or odd time of arrival/departure - taxis may not always be available.
www.parishuttle.com - I use them monthly from Paris to and from CDG and ORY - online reservation and they will speak English.