No, not really. All else being equal:
I'd say that today, it's much muddier than it was maybe ten years ago, before the data science explosion and cloud explosion.
That is, turn-key cloud Postgres is not Y2K Postgres, and MySQL post-Maria is not Y2K MySQL. In the former, administration of Postgres has gotten much easier since Heroku got involved and Andy Pavlo started talking about self-driving databases. In the latter, MySQL can do text search well enough that I sat pair programming this with a young engineer around 2016-2017 when I'd have argued prior that you were wasting your time.
In the end, it probably comes down to how you rank your requirements:
usability, performance, suitability for a particular purpose.
Things like postgis and pgrouting may have little equal, so like others, those can be huge differentiators if you need them and see the advantage in db backend computation without invoking the N+1 query problem in aggregate.
I'm biased since I used MySQL before the inefficient backend was deprecated and I used PostgreSQL to do all manner of experimental EAV implementations using bjson including various forms of tuples from Rich Hickey.
All hail Stonebraker.