What you're really trying to do is subtract one set from another set. Hashes are the right tool, but this can be done with slices instead of loops. 
# find old values that are not in new values
my %deletions;
@deletions{@oldvalues} = ();
delete @deletions{@newvalues};
my @deletions = keys %deletions;

# find new values that are not in old values
my %additions
@additions{@newvalues} = ();
delete @additions{@oldvalues};
my @additions = keys %additions;

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Update: fixed hash names.

In reply to Re: comparing two hashes by chipmunk
in thread comparing two hashes by Cody Pendant

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