Sorting Linked Lists - move nodes or swap data members?

I have a simple question. I'm working on a C++ app that is a contact list app. It stores names, addresses, numbers, ages, etc for multiple people. I'm using stucts and linked lists (nodes). I'm building the sort list function, to alphabetize the list. I'm currently wondering if it's better to actually reorder the list by moving the structs as a whole or by swapping the data members inside each node. At first, I considered moving the nodes, but now swapping the data members seems more safe, as I don't have to reorder the list. At any rate, I don't know if either possesses any benefits over the other.I have a simple question. I'm working on a C++