Perceptive mobile networks (PMNs) implement sensing and communication by reusing existing cellular infrastructure. Thanks to the cooperation among distributed access points, cell-free multiple-input multiple-output (MIMO) systems support the deployment of multistatic radar sensing, while providing high spectral efficiency for data communication services. To this end, in a cell-free MIMO system, distributed access points (APs) communicate over fronthaul links with a central processing unit (CPU) in the cloud. This work proposes four different types of PMN uplink solutions based on cell-free MIMO systems, in which the sensing and decoding functionalities are carried out at either the cloud or the edge. Accordingly, we develop 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 for fronthaul quantization to maximize the achievable rate under sensing 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.