I'm not sure what algorithm sort uses, but in general, it's a bad idea not to implement identity whenever you write a comparision function.

In your example, the function will always return -1 for the three sets of identical pairs - something that will result in interesting sort orders, depending on the algorithm used.

You should at least rewrite the routine like this :

sub by_priority {
  # Return 0 on string identity
  return 0 if $a eq $b;

  return -1 if $a =~ /^Organization/ ;
  return  1 if $b =~ /^Organization/ ;
  return -1 if $a =~ /^Service/ ;
  return  1 if $b =~ /^Service/ ;
  return -1 if $a =~ /^FAQ/ ;
  return  1 if $b =~ /^FAQ/ ;

  return  0 ;

}
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My personal favourite when rewriting that code would be via grep :

my @priorities = qw(Organization FAQ Service);
my $prio_top = join "|", map { "^$_" } @priorities;
sub by_priority {
  # Return 0 on string identity
  return 0 if $a eq $b;

  return -1 if $a =~ /$prio_top/o;
  return  1 if $b =~ /$prio_top/o;

  # Alphabetical sort for the rest
  return $a cmp $b;
}
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If you're concerned with raw sort speed (for many values), a Guttman-Rosler-Transform would be the best thing - you simply encode the priorities together with each item in a string, let sort rip through it and unpack it afterwards.

If you're not tied to your current algorithm, it might be a good idea to first partition your dataset into the four categories, indivitually sort them and afterwards simply concatenate them together.

perl -MHTTP::Daemon -MHTTP::Response -MLWP::Simple -e ' ;    # The  
$d = new HTTP::Daemon and fork and getprint $d->url and exit;#spider
($c = $d->accept())->get_request(); $c->send_response( new   #in the
HTTP::Response(200,$_,$_,qq(Just another Perl hacker\n))); ' #  web
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