It has been shown that networks of memristors are promising as computing medium for the solution of complex optimization problems. In this context, the solution to the shortest-path problem (SPP) in a two-dimensional plane has been given wide consideration. Some still open problems in such computing approach concern the time required for the network to reach to a steady state, and the time required to read the result, stored in the state of a subset of memristors that represent the solution. This paper presents a circuit simulation-based performance assessment of memristor networks as SPP solvers. A previous methodology is extended to support weighted directed graphs. We use memristor device models with fundamentally different switching behavior, to check their suitability for such applications. Furthermore, the requirement of binary vs. analog operation of memristors is evaluated. Finally, this approach is compared to known algorithmic solutions to the SPP over a set of large random graphs. Our results contribute to the development of bio-inspired memristor network-based SPP solvers.