The impact of autonomous vehicles (AVs) on urban mobility systems is an increasingly discussed topic in recent years. There is currently some discussions about different ownership models and their consequences. Regarding autonomous vehicles (AVs), two ownership models are being considered for future transportation systems. These are: autonomous vehicles as a public service or individual owning ownership. The first ownership model is based on AVs operating within an on-demand (taxi) service while the second proposes private vehicle ownership combined with offering the AV to other users when not used by its owner and thereby partially financing the vehicle's acquisition cost. In addition to the ownership model comes the possibility of sharing rides. The main difference when sharing a trip is that an individually-owned vehicle always prioritizes its owner. Based on an existing approach for assessing the potential of predefined meeting points in a ride-sharing service, we develop a method for assessing the sharing potential of those different variants. We consider the number and distance of shared trips, and thus, we evaluate the potentially saved vehicle kilometers. We analyze several ownership and sharing scenarios on a case study for New York and Paris. The results demonstrate that sharing AV trips has the potential of increasing the system-wide matching rate as well as saving up to 25% of the overall traveled distance.