Choose whichever one you/your team is more familiar with. Both are battle-tested and proven and will likely scale to whatever needs you have.
Whichever one you start out with, you will be annoyed if you switch to the other one 5 years later. I started out with mysql, and when I started working on a postgres project, I was shocked at some of the ways it was lacking (how am I supposed to store email addresses in a database without collations?).
But when postgres folks grouse about stuff in mysql, I'm usually nodding along and saying "yeah, that would be nice".
They're both great options. If anybody on your team is already an expert at one of them, use that one.
How long ago was this? :)
The documentation of Postgres 11 [2] states that this was not possible:
Note that while this system allows creating collations that “ignore case” or “ignore accents” or similar (using the ks key), PostgreSQL does not at the moment allow such collations to act in a truly case- or accent-insensitive manner. Any strings that compare equal according to the collation but are not byte-wise equal will be sorted according to their byte values.
Not familiar with MySQL so trying to look that up, but with a constraint? Or just don't do that? - SO answer I found says 'it's much more useful to have johndoe@ and JohnDoe@ treated as the same than it is to support case sensitive email addresses'.. ok, it's also incompliant, but whatever's 'more useful’ I guess!
I will also add that their are giant companies relying on both databases with great success. Facebook still runs on MySQL, and contribute back to it. Youtube I'm not sure about, but it did run on MySQL for a long time, well after it got massive. I'm sure examples exist for Postgres (Amazonm since they moved off Oracle?)