If your project is already on MySQL and you have no issue => Don't change anything
If your project is already on MySQL and you have issues => understand the issues you are facing and make sure that moving to Postgres would fix them (99% chance it won't)
If you have a new project and have very precise informations about the constraint you will face (pretty rare) => Do your research and choose what's best for your use case
If you have a new project and have only got a vague idea of what you are going to need/face 5 years down the road => Postgres is a slightly better choice than MySQL due to the feature set. Unless you have some other reason to go for MySQL (expertise, ...)
If your project is already on MySQL and you have issues => understand the issues you are facing and make sure that moving to Postgres would fix them (99% chance it won't)
If you have a new project and have very precise informations about the constraint you will face (pretty rare) => Do your research and choose what's best for your use case
If you have a new project and have only got a vague idea of what you are going to need/face 5 years down the road => Postgres is a slightly better choice than MySQL due to the feature set. Unless you have some other reason to go for MySQL (expertise, ...)