I'd go for Time::Local -- it's simple and direct: convert each string to "seconds since the epoch" and subtract. The only downside is having to relate month names to numbers.

use Time::Local;

my $beginning = 'Thu Oct 24 17:37:58 2007';
my $end       = 'Fri Oct 26 06:54:09 2007';
my %month = ( Jan => 0, Feb => 1, Mar => 2,
              Apr => 3, May => 4, Jun => 5,
              Jul => 6, Aug => 7, Sep => 8,
              Oct => 9, Nov => 10, Dec => 11 );

for ( $beginning, $end ) {
    my ( $mo, $dy, $hr, $mi, $se, $yr ) = ( split /[\s:]/ )[1..6];
    $mo = $month{$mo};
    $_ = timelocal( $se, $mi, $hr, $dy, $mo, $yr );
}

printf "%d sec elapsed\n", $end - $beginning;
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That's just a very crude demonstration, but it gives you an idea what needs to be done.

update: here's a more perlish way to initialize month numbers:

my $i=0;
my %month = map {$_=>$i++} qw/Jan Feb Mar Apr May Jun Jul Aug Sep Oct 
+Nov Dec/;
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