Logging: stderr vs syslog?

I've just inherited a few PostgreSQL DBs, having come from Oracle land. I'm
looking to shore up the logging situation. Right now we use stderr logging
and they get rotated based on size threshold. I'd like for those old logs
to be gzipped so we can keep more on disk rather than current method of
just deleting old logs to free up space. This is mostly on pgsql 9.2 with a
couple of 9.3, but I'm planning to upgrade everything to 9.6.3 when I get
my feet on solid ground.

Couple of question around this:

1. I thought logrotate would be a no-brainer here, but it sounds like I
should then change to use syslog rather than stderr. I've read some caveats
around syslog needing to sync files and potentially slow things down. I'm
wondering if any grizzled production postgres veterans could offer up their
experience.
2. Alternatively I could just keep it going with stderr and have a
separate script run find/gzip on log files beyond a certain mtime
threshold. This would probably be the quickest to implement, but I'd much
rather use logrotate facilities if there are no strong opinions against
using syslog.

Thanks in advance for your time, I'm sure I'll be making a lot of us of
these mailing lists in the not-too-distant future.

Don.

--
Don Seiler
www.seiler.us