Why are you using eq in one comparison and > in the other? Besides, using cmp you can avoid the duplicate comparison altogether. Your looping condition is not robust, either.

my @array1 = sort <$file1>;
my @array2 = sort <$file2>;

my ($l,$r) = (0) x 2;

while ($l < @array1 and $r < @array2) {
    if(my $b = $array1[$l] cmp $array2[$r]) {
        ++($b == 1 ? $r : $l);
    }
    else {
        print "Dupe: $array1[$l]\n";
        ++$l;
        ++$r;
    }
}
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Makeshifts last the longest.