Local energy communities and electricity markets have emerged as possibilities for interaction among prosumers. A substantial effort has been invested into creating efficient pricing mechanisms for various market arrangements, all of which take into consideration distinct characteristics of local electricity trading. However, since they are all evaluated in terms of various systems and market conditions, it is challenging to directly compare the mechanisms. In this research, three well-established pricing mechanisms from the literature are systematically compared and evaluated under identical settings on their influence on welfare distribution across various market participant groups, privacy protection, transparency and complexity level. According to the findings, the supply-demand ratio pricing system leads to the lowest costs for consumers and is also the most privacy compliant and transparent. Furthermore, prosumers obtain the highest cost-savings through the consensus alternating direction method of multipliers pricing mechanism, whereas the equilibrium pricing mechanism performs best regarding economic fairness. The aim of this article is to provide insight into the performance of different pricing mechanisms to energy regulators and local electricity market facilitators. The comparative analysis should aid in making informed decisions on the implementation of local electricity markets.