I've heard MySQL (well, MariaDB, really) has improved a lot in recent years, but I still can't imagine why I'd ever choose it over Postgres for a professional project. Is there any reason?
It used to be that bargain basement shared-hosting providers would only give you a LAMP stack, so it was MySQL or nothing. But if you're on RDS, Postgres every time for my money.
For MySQL, I haven't found anything that beats SequelPro. For Postgres, I haven't found anything that comes close to parity, but my favorite is Postico.
I know people that swear by IntelliJ for their db stuff, it just never hit home for me personally though.