While your earlier comments indicate that you're more interested in parsing than the mechanics of date comparison (and for that the regex is just what you're looking for), it's worth mentioning that converting the dates to julian dates (the total number of days or seconds or whatever since some date a long time ago) makes comparisons easy and intuitive. And, based on the comments of the author of Date::Calc, if you need to compare a very large number of dates, you would probably see some good performance gains from using Time::JulianDay over Date::Calc. Here's how you'd do it:

#!/usr/bin/perl
use Time::JulianDay;
my $date0 = '5/2/2000';
my $date1 = '12/12/2001';
print &check_dates($date0,$date1) ? "$date0 > $date1\n" : "$date0 < $date1\n";
sub check_dates {
        my ($date0,$date1) = @_;
        if ($date0 =~ m|\d{1,2}/\d{1,2}/\d{4}| && $date1 =~ m|\d{1,2}/\d{1,2}/\d{4}|) {
                $date0 =~ m|(\d{1,2})/(\d{1,2})/(\d{4})|;
                my $jd0 = julian_day($3,$2,$1);
                $date1 =~ m|(\d{1,2})/(\d{1,2})/(\d{4})|;
                my $jd1 = julian_day($3,$2,$1);
                return $jd0 > $jd1 ? 1 : 0;
        }
}

Hope this helps!