Perceptive mobile networks implement sensing and communication by reusing existing cellular infrastructure. Cell-free multiple-input multiple-output, thanks to the cooperation among distributed access points, supports the deployment of multistatic radar sensing, while providing high spectral efficiency for data communication services. To this end, the distributed access points communicate over fronthaul links with a central processing unit acting as a cloud processor. This work explores four different types of PMN uplink solutions based on Cell-free multiple-input multiple-output, in which the sensing and decoding functionalities are carried out at either cloud or edge. Accordingly, we investigate and compare joint cloud-based decoding and sensing (CDCS), hybrid cloud-based decoding and edge-based sensing (CDES), hybrid edge-based decoding and cloud-based sensing (EDCS) and edge-based decoding and sensing (EDES). In all cases, we target a unified design problem formulation whereby the fronthaul quantization of signals received in the training and data phases are jointly designed to maximize the achievable rate under sensing requirements and fronthaul capacity constraints. Via numerical results, the four implementation scenarios are compared as a function of the available fronthaul resources by highlighting the relative merits of edge- and cloud-based sensing and communications. This study provides guidelines on the optimal functional allocation in fronthaul-constrained networks implementing integrated sensing and communications.