MySQL has no custom extensions, which sucks because it limit's it's functionality to the things the development team think to be important, which upto now has been pretty much nothing. Yes, I hate the limts MySQL forces on you, deal with it.
PostgreSQL on the other hand welcomes new development and it's extension features mean that anyone can create an extension that every PostgreSQL user can deploy.
This gives rise to a lot of exciting features, like PGStrom
PGStrom connects postgresql's queryparser to your GPU to offload work to it, increasing the processing speed through parallelization, and freeing up precious CPU resources. Complex JOIN operations that basically require endless looping through data can be sped up by using a GPU that hasa much higher memory-bandwidth, and which has been designed to do simple boring tasks.
This means that you can increase the performance of a single server, saving you the hassle of scaling out to multiple servers or increasing the number of CPU's per server (which requires different hardware, more memory, more everything per server).