There is another case where the two possibilities differ, on top of those already mentioned: if you need to call a non-public constructor (protected or private), make_shared might not be able to access it, while the variant with the new works fine.
class A
{
public:
A(): val(0){}
std::shared_ptr<A> createNext(){ return std::make_shared<A>(val+1); }
// Invalid because make_shared needs to call A(int) **internally**
std::shared_ptr<A> createNext(){ return std::shared_ptr<A>(new A(val+1)); }
// Works fine because A(int) is called explicitly
private:
int val;
A(int v): val(v){}
};