To echo a few other commenters here, a major point of consideration is your team's experience and broader technical network. Generally speaking, either Postgres or MySQL is likely fine for most applications. But you'll have a better time with whichever one you can most smoothly build on, operate, and hire for.
Separate from that, and with the disclaimer that my career has been heavily MySQL-oriented, although I try to provide a balanced perspective:
MySQL can be a good choice for OLTP-heavy workloads, such as a high volume of relatively straightforward queries. It also supports a very wide variety of replication options. In some aspects, MySQL is simpler to operate than pg. (This can be a point of contention, as MySQL is more idiosyncratic and this leads to some land-mines that are well-known to the community, but unclear from the manual alone.)
At this point there are also many hundreds (thousands?) of engineers and DBAs worldwide who have extensive experience working on massive-scale MySQL deployments. This may or may not be relevant to your project, depending what you're building and its eventual best-case size.
MySQL is admittedly less "batteries included". Although MySQL/InnoDB does support things like windowing functions, fulltext, geospatial, etc they're not necessarily a best-in-class implementation yet. In a MySQL shop, if you need OLAP, you're better off doing ETL into a separate column store or Hadoop cluster; if you need fulltext search, you're better off using a separate search index system like Solr; etc. Depending on your point-of-view, this approach is either "more UNIXy" or a major operational headache, or both :)
Meanwhile Postgres may be a better choice if you want to handle a bunch of things using a single piece of software: mixed OLTP + OLAP workloads, fulltext search, geospatial. It also has some interesting indexing features MySQL lacks, such as partial indexes, and ability to index an entire nested JSON structure in a single index.
Postgres gets major points for having a true open source development model, cleaner core code, better adherence to SQL standards, etc. Conceptually, it is very well-aligned with the textbook description of a relational database. Its adherents love it, sometimes fanatically so, which can be a mixed bag to outsiders. I sometimes feel parallels to the Mac user community in the late 90s/early 00s: it's probably a better choice for many use-cases, but personally I raise an eyebrow to suggestions that it's the universal best choice for all possible situations.