You may be confusing InnoDB with MyISAM (which is prone to corruption, especially upon crashes) or with running MySQL without a strict SQL mode (which causes bad things like silent truncation of overflowing values).
InnoDB is, and always has been, a very reliable and durable storage engine with solid performance characteristics.
Re:PostgreSQL 9.6 Released
by MustardTiger on Thursday September 29, 2016 @08:30PM
(#12609827)
No, I am referring to innodb, which has a number of known reliability problems which are "wontfix".
What? Everyone speaks about how unreliable it is and how many major data corruption problems it has.
>I have never heard much about storage engines in Postgres, why could this be so?
Because they didn't take the approach of having multiple storage engines, they just made one that works and is not easily removed from the database.