Most robust would be to have the syslog server be a broadcast address on a small subnet, where there are two LINUX boxes providing redundant syslog service. Syslog should use udp packets, so both machines will log the same packets.
Logging on every syslog server is controlled by the configuration file, which specifies key filters for each configured output file.
Man Page for syslog.conf (all Section 4) - The UNIX and Linux Forums
Man Page for syslogd (all Section 1m) - The UNIX and Linux Forums
If the syslog is configured remote, the local server should not be seeing the packets, unless it is double-logging.
I usually google for tutorials to get started.
syslog tutorial - Google Search