I'd use List::Compare (though I'm not sure I like its object-oriented interface):
#!/usr/bin/perl
use strict;
use warnings;
use feature qw/say/;
use List::Compare;
use List::MoreUtils qw/uniq/;
my %hash1 = ("abc" => [1, 2, 3, 4]);
my %hash2 = ("abc" => [1, 3, 5, 7]);
$, = ",";
foreach my $key (uniq (keys %hash1, keys %hash2)) {
my $lc = List::Compare->new($hash1{$key} // [], $hash2{$key} // []
+);
say $lc->get_Lonly; # elements only in $hash1{$key}
say $lc->get_Ronly; # elements only in $hash2{$key}
}