I would look at the interface of std::list, which is a C++ implementation of linked lists. It seems that you are approaching the templating of your Linked list class wrong. Ideally your linked list should not care about ownership semantics (i.e. whether it is instantiated with raw ptrs, smart pointers or stack allocated variables). An example of ownership sematics with STL containers follows. However, there are better examples of STL and ownership from more authoritative sources.
#include <iostream>
#include <list>
#include <memory>
using namespace std;
int main()
{
// Unique ownership.
unique_ptr<int> int_ptr = make_unique<int>(5);
{
// list of uniquely owned integers.
list<unique_ptr<int>> list_unique_integers;
// Transfer of ownership from my parent stack frame to the
// unique_ptr list.
list_unique_integers.push_back(move(int_ptr));
} // list is destroyed and the integers it owns.
// Accessing the integer here is not a good idea.
// cout << *int_ptr << endl;
// You can make a new one though.
int_ptr.reset(new int(6));
// Shared ownership.
// Create a pointer we intend to share.
shared_ptr<int> a_shared_int = make_shared<int>(5);
{
// A list that shares ownership of integers with anyone that has
// copied the shared pointer.
list<shared_ptr<int>> list_shared_integers;
list_shared_integers.push_back(a_shared_int);
// Editing and reading obviously works.
const shared_ptr<int> a_ref_to_int = list_shared_integers.back();
(*a_ref_to_int)++;
cout << *a_ref_to_int << endl;
} // list_shared_integers goes out of scope, but the integer is not as a
// "reference" to it still exists.
// a_shared_int is still accessible.
(*a_shared_int)++;
cout << (*a_shared_int) << endl;
} // now the integer is deallocated because the shared_ptr goes
// out of scope.
A good exercise to understand ownership, memory allocation/deallocation, and shared pointers is to do a tutorial where you implement your own smart pointers. Then you will understand exactly how to use smart pointers and you will have one of those xen moments where you realise how pretty much everything in C++ comes back to RAII (ownership of resources).
So back to the crux of your question. If you want to stick to Nodes of type T, don't wrap the node in a smart pointer. The Node destructor must delete the underlying raw pointer. The raw pointer may point to a smart pointer itself specified as T. When your "LinkedList"'s class destructor is called it iterates through all Nodes with Node::next and calls delete node;
after it obtained the pointer to the next node.
You could create a list where nodes are smart pointers... but this is a very specialised linked list probably called SharedLinkedList or UniqueLinkedList with very different sematics for object creation, popping, etc. Just as an example, a UniqueLinkedList would move a node in the return value when popping a value to a caller. To do metaprogramming for this problem would require the use of partial specialization for different types of T passed. Example, something like:
template<class T>
struct LinkedList
{
Node<T> *head;
};
// The very start of a LinkedList with shared ownership. In all your access
// methods, etc... you will be returning copies of the appropriate pointer,
// therefore creating another reference to the underlying data.
template<class T>
struct LinkedList<std::shared_ptr<T>>
{
shared_ptr<Node<T>> head;
};
Now you start implementing your own STL! You can already see potential for problems as mentioned in the comments to your question with this approach. If nodes have shared_ptr next it will result in a call to that shared Node's destructor, which will call the next shared Node destructor and so forth (stack overflow due to the recursion is possible). So that is why I don't care much for this approach.