Due to the growing number of Distributed Energy Resources and new electrical loads at the sectoral contact points, novel organisational forms such as Local Energy Markets arise to deal with increasing complexity in the energy system. However, these markets are radically different from traditional energy markets, as they often allow individual prosumers to trade with each other via a peer-to-peer scheme. To guarantee tamperproof settlement, an increasing number of these markets feature a distributed ledger technology. This paper analyses different design variants of peer-to-peer markets, focusing specifically on the allocation mechanism under network constraints as these mechanisms constitute the core component of a market design. We assess these designs concerning user acceptance, economic performance, practicability, and their ability to relieve grid congestion. Further key performance indicators also cover communal revenues or welfare distribution. For this purpose, we developed an agent-based simulation framework, which builds on data from three German reference municipalities derived from a novel clustering approach. Besides a consolidated presentation of the results, we highlight current implementation obstacles and identify promising concepts for further research.