looks like you want the symmetric difference of two character sets

  DB<111> @a1=split//,$str1
 => ("A", "B", "C", "D", "E")

  DB<112> @a2=split//,$str2
 => ("B", "C", "D", "E", "O")

  DB<113> @h2{@a2}=()

  DB<114> @h1{@a1}=()

  DB<115> delete @h2{@a1}

  DB<116> delete @h1{@a2}

  DB<117> (keys %h1, keys %h2)
 => ("A", "O")
[download]

see Using hashes for set operations... for background.

UPDATE:

seems like nobody mentioned that its a FAQ How do I compute the difference of two arrays? How do I compute the intersection of two arrays?

UPDATE:

Just in case you only want the unique characters in both strings:

  DB<137> $h{$_}++ for (split//,$str1),(split//,$str2)
 => ""

  DB<138> \%h
 => { A => 1, B => 2, C => 2, D => 2, E => 2, O => 1 }

  DB<139> grep {$h{$_}==1} keys %h
 => ("A", "O")
[download]

oops basically already shown by Not_a_Number

EDIT: one liner =)

  DB<146> grep {$h{$_}==1} map {$h{$_}++;$_} split//,$str1.$str2
 => ("A", "O")
[download]