I totally agree that benchmarks with different parameters are fairly meaningless. Was just trying to give people a ballpark figure in reply to the question about how to 2 compare with benchmarks; even if they are not equivalent.
One interesting point about this is that the PostgreSQL benchmark tops out at 8 users whereas the MySQL ones start around 8 users and go up from there. Right at the 8 user point, both SQL engines are within the same range, just under 100k QPS on read; with the hardware (# of cores) not changing this value much, as well as the MySQL version 5.5-5.7 not having any effect either. That seems like a limit that these 2 SQL engines (PostgreSQL & MySQL) are hitting; most likely from parsing the SQL. Thus the only way to improve single threaded performance is to use something other than SQL; like the memcache protocol.
IMHO the assumption that parsing the SQL is the bottleneck here is unfounded - I'd like to see some analysis supporting that first. The queries used in those benchmarks are extremely trivial, and there are far more expensive operations involved. I don't think it can be deduced from comparison of two quite different benchmarks (different workloads, different dataset sizes, different hardware, ...)
Also, relational databases are general-purpose query engines, not caching solutions like memcached, with very limited set of commands. It might be possible to invent a more efficient binary protocol to send queries/receive results, but then you still have things like optimization, planning, permission checks, ... that are usually more expensive than parsing the data.
It's almost certainly not SQL parsing that is introducing a serial component and an upper bound on parallelism. Actually, that is a task that is almost perfectly parallelizable. Parsing has no serial component, planning may have one if you somehow need locks on shared data structures needed for plan optimization.
MySQL and Postgresql are insanely different. To a point that it's uninteresting to compare them. MySQL is a keystore with an SQL frontend, which eventually got ACID features bolted on. Postgresql is a full-fledged RDBMS that eventually got refactored with performance in mind. While the end goal seems the same, the results are really different.
All of this text to say something which I think is common knowledge and is found interspersed in the comments here. For any kind of moderately complex query, Postgresql will eat Mysql's lunch. For any kind of concurrent locking, highly parallel, use case, Postgresql is much faster and/or safer. For any kind of very simple query, Mysql will eat Postgresql's lunch. It's a result of different upbringings.
If your use case can be satisfied with memcache, you aren't using a relational database and, yes, Mysql is the best choice, out of these two. Anyhow, in this scenario, today, there is a vast choice of good persistent keystores that are better than mysql.