I usually find it easier to compare lists using hashes, like so:

sub different
{
    my ($h1, $h2) = @_;
    return 1 unless keys %$h1 == keys %$h2;
    for (keys %$h1) {
        return 1 unless exists $h2->{$_};
    }
    return 0;
}

sub member {
    my ($a, $aoa) = @_;
    my %as;
    undef @as{@$a};
    for my $x (@$aoa) {
        my %bs;
        undef @bs{@$x};
        return 1 unless different \%as, \%bs;
    }
    return 0;
}
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Depending on what else you're doing with the AoA, you might want to use an array of hashes instead.