my $date1 = "2003-05-20";
my $date2 = "2003-04-19";

if ($date1 gt $date2) { print "Date 1 is bigger" }

# # # alternatively
my $date1 = "2003-05-20";
my $date2 = "2003-04-19";

$date1 =~ s/\-//g;
$date2 =~ s/\-//g;

if ($date1 > $date2) { print "Date 1 is bigger" }