There is an increased interest from transit agencies to replace fixed-route transit services with on-demand public transits (ODT). However, it is still unclear when and where such a service is efficient and sustainable. To this end, we provide a comprehensive framework for assessing the sustainability of ODT systems from the perspective of overall efficiency, environmental footprint, and social equity and inclusion. The proposed framework is illustrated by applying it to the Town of Innisfil, Ontario, where an ODT system has been implemented since 2017. It can be concluded that when there is adequate supply and no surge pricing, crowdsourced ODTs are the most cost-effective transit system when the demand is below 3.37 riders/km2/day. With surge pricing applied to crowdsourced ODTs, hybrid systems become the most cost-effective transit solution when demand ranges between 1.18 and 3.37 riders/km2/day. The use of private vehicles is more environmentally sustainable than providing public transit service at all demand levels below 3.37 riders/km2/day. However, the electrification of the public transit fleet along with optimized charging strategies can reduce total yearly GHG emissions by more than 98%. Furthermore, transit systems have similar equity distributions for waiting and in-vehicle travel times.