In the first case you are processing the log 40+ times.

In the second case you are are accumulating a *lot* of data in memory.

The third option is to open the 40 output files and process the log once, writing to the appropriate file as you determine it. Something like this (untested).

#! perl -slw
use strict;

my @deptids = qw[ dept1 dept2 dept3 ];
my %fh;

open $fh{ $_ }, '+>', "/data/logs/${_}current.log" 
    or die "$_: $!" 
    for @deptids;

open (LOGFILE, "/data/logs/access.log") or die $!;

while( defined( my $line = <LOGFILE> ) ) {
    my $match;
    for( @deptids ) { $match = $_ and last if $line =~ m[\Q$_] };
    if( $match ) {
        ## Note: The {}s around the file handle are required.
        print { $fh{ $match } } $line;
    }
    else {
        print STDERR "'$line' didn't match any dept";
    }
}
close $_ for values %fh;

close LOGFILE;
[download]

Create an hash of department => IO::File object for that department's log. Read through the main log, determinining what department the entry is for and printing to the corresponding object.

my %handles;
for my $dept ( @departments ) {
  $handles{ $dept } = IO::File->new;
  $handles{ $dept }->open( "> $logdir/$dept.log" ) or die "Open failed
+: $!\n";
}

while( <INLOG> ) {
  my $dept = divine_department( $_ );
  $handles{ $dept }->print( $_ );
}
[download]

Your second solution got the log procesesing down to a single pass and then uses memory to hold the data. For "small" logs this will work, but you will run out of memory as the log gets larger. The real solution, as Fletch pointed out, is to write the data once you have determined where it should go into an extract file (one per department). The code Fletch proposes will scale nicely, as you add more departments (another bonus).

As to the amount of time it takes, you said "I have a very large Apache log...". There is a basic Principle of Science to bear in mind here:

TTT -- Things Take Time.