Should operator<< be implemented as a friend or as a member function?

friend bool operator<<(obj const& lhs, obj const& rhs);

ostream& operator<<(obj const& rhs);

friend ostream & operator<<(ostream &os, const Paragraph& p) {
    return os << p.to_str();
}

ostream & operator<<(ostream &os) {
    return os << paragraph;
}

Paragraph::to_str = (return paragraph)

#include <iostream>

class Paragraph
{
    public:
        Paragraph(std::string const& init)
            :m_para(init)
        {}

        std::string const&  to_str() const
        {
            return m_para;
        }

        bool operator==(Paragraph const& rhs) const
        {
            return m_para == rhs.m_para;
        }
        bool operator!=(Paragraph const& rhs) const
        {
            // Define != operator in terms of the == operator
            return !(this->operator==(rhs));
        }
        bool operator<(Paragraph const& rhs) const
        {
            return  m_para < rhs.m_para;
        }
    private:
        friend std::ostream & operator<<(std::ostream &os, const Paragraph& p);
        std::string     m_para;
};

std::ostream & operator<<(std::ostream &os, const Paragraph& p)
{
    return os << p.to_str();
}


int main()
{
    Paragraph   p("Plop");
    Paragraph   q(p);

    std::cout << p << std::endl << (p == q) << std::endl;
}

ostream & operator<<(ostream &os) {
    return os << paragraph;
}

// T << Paragraph
T & operator << (T & p_oOutputStream, const Paragraph & p_oParagraph)
{
   // do the insertion of p_oParagraph
   return p_oOutputStream ;
}

// T >> Paragraph
T & operator >> (T & p_oInputStream, const Paragraph & p_oParagraph)
{
   // do the extraction of p_oParagraph
   return p_oInputStream ;
}

// T << Paragraph
T & T::operator << (const Paragraph & p_oParagraph)
{
   // do the insertion of p_oParagraph
   return *this ;
}

// T >> Paragraph
T & T::operator >> (const Paragraph & p_oParagraph)
{
   // do the extraction of p_oParagraph
   return *this ;
}

// OUTPUT << Paragraph
template <typename charT, typename traits>
std::basic_ostream<charT,traits> & operator << (std::basic_ostream<charT,traits> & p_oOutputStream, const Paragraph & p_oParagraph)
{
   // do the insertion of p_oParagraph
   return p_oOutputStream ;
}

// INPUT >> Paragraph
template <typename charT, typename traits>
std::basic_istream<charT,traits> & operator >> (std::basic_istream<charT,traits> & p_oInputStream, const CMyObject & p_oParagraph)
{
   // do the extract of p_oParagraph
   return p_oInputStream ;
}

// OUTPUT << A
std::ostream & operator << (std::ostream & p_oOutputStream, const Paragraph & p_oParagraph)
{
   // do the insertion of p_oParagraph
   return p_oOutputStream ;
}

// INPUT >> A
std::istream & operator >> (std::istream & p_oInputStream, const Paragraph & p_oParagraph)
{
   // do the extract of p_oParagraph
   return p_oInputStream ;
}

bool operator<<(const obj&, const obj&);

ostream& operator<<(ostream&, const obj&);