What’s the benefit of std::back_inserter over std::inserter?

Iterator types

• std::back_inserter returns std::back_insert_iterator that uses Container::push_back().
• std::inserter returns std::insert_iterator that uses Container::insert().

std::list

For lists std::list::push_back is almost the same as std::list::insert. The only difference is that insert returns iterator to inserted element.

bits/stl_list.h

void push_back(const value_type& __x)
  { this->_M_insert(end(), __x); }
void _M_insert(iterator __position, const value_type& __x)
  {
    _Node* __tmp = _M_create_node(__x);
    __tmp->_M_hook(__position._M_node);
  }

bits/list.tcc

template<typename _Tp, typename _Alloc> typename list<_Tp, _Alloc>::iterator
list<_Tp, _Alloc>::insert(iterator __position, const value_type& __x)
  {
  _Node* __tmp = _M_create_node(__x);
  __tmp->_M_hook(__position._M_node);
  return iterator(__tmp);
  }

std::vector

It looks a little different for std::vector. Push back checks if reallocation is needed, and if not just places value in correct place.

bits/stl_vector.h

void push_back(const value_type& __x)
  {
  if (this->_M_impl._M_finish != this->_M_impl._M_end_of_storage)
    {
    _Alloc_traits::construct(this->_M_impl, this->_M_impl._M_finish, __x);
    ++this->_M_impl._M_finish;
    }
  else
    _M_insert_aux(end(), __x);
  }

But in std::vector::insert there are 3 additional things done and it impacts performance.
bits/vector.tcc

template<typename _Tp, typename _Alloc> typename vector<_Tp, _Alloc>::iterator
vector<_Tp, _Alloc>::insert(iterator __position, const value_type& __x)
  {
  const size_type __n = __position - begin(); //(1)
  if (this->_M_impl._M_finish != this->_M_impl._M_end_of_storage
  && __position == end()) //(2)
    {
    _Alloc_traits::construct(this->_M_impl, this->_M_impl._M_finish, __x);
    ++this->_M_impl._M_finish;
    }
  else
    {
    _M_insert_aux(__position, __x);
    }
  return iterator(this->_M_impl._M_start + __n); //(3)
  }