It doesn’t make a difference as far as construction of the new object is concerned; you already have a unique_ptr<Foo> prvalue (the result of the call to make_unique) so both push_back and emplace_back will call the unique_ptr move constructor when constructing the element to be appended to the vector.
If your use case involves accessing the newly constructed element after insertion, then emplace_back is more convenient since C++17 because it returns a reference to the element. So instead of
my_vector.push_back(std::make_unique<Foo>("constructor", "args"));
my_vector.back().do_stuff();
you can write
my_vector.emplace_back(std::make_unique<Foo>("constructor", "args")).do_stuff();