Assuming the strings are fairly short and contain a limited number of unique characters, which is likely in this case:

print diffCount('aaaaacaacaaagcc', 'acaggtgacaaaaaa');

sub diffCount {
    my (%counts, $sum, $i);

    $counts{substr($_[0], $_, 1)}++ for 0..(length($_[0]) - 1);
    $counts{substr($_[1], $_, 1)}-- for 0..(length($_[1]) - 1);

    $sum += abs $_ for values %counts;

    return $sum;
}
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I tried other methods using split, regex, etc., but this benchmarked the fastest. Obviously, doing the same thing in C or C++ would be even faster.