use Email::Address;

my @addresses = map { Email::Address->parse($_) } <DATA>;

print is_equivalent(@addresses) ? '' : 'not ' , "equivalent\n";

sub is_equivalent {
    my ($a, $b) = @_;

    return lc $a->address eq lc $b->address;
}

__DATA__
"John Doe" <jdoe@bla.com> (Johnnie "Two Toes")
jDOE@BLA.COM