Either method is possible; I'd prefer the second with apcaccess as it describes the actual status of the UPS while the log could be delayed / overwritten / have other, meaningless lines. You also seem to have it in your script but commented out. Unfortunately, I don't know apcaccess and so can't tell which info indicates a "power out" status and maybe more (mayhap on top of "STATUS: ONLINE", one of the bits in STATFLAG might give deeper insight?).
Assuming it were the STATUS line, and stealing from your script, try (untested, and not sure the sh shell will correctly run this, you may need e.g. bash)

Code:

sleep 10
/sbin/apcaccess status > /tmp/TMP$$
! grep -q "STATUS   : ONLINE" /tmp/TMP$$ && echo mail -s $MSG  $SYSADMIN </tmp/TMP$$
rm /tmp/TMP$$

Remove the echo when happy with the result.


Final comment: the "shebang" in your script #!/bin/sh needs to be in the very first line to become effective, i.e. determines the shell to be run to execute your code.