Would also add that Proof-of-Work is the only proven method today to ensure consensus. Proof-of-Stake has it's flaws, it's a preferable system and people are working to make it happen, because PoW wastes a damn lot of energy, but that's exactly what makes PoW so strong.
You have to be very deep-pocketed just to attempt altering current btc blocks, and nothing less than nation-state level to change blocks a 12 hours old, beyond a few days it's computationally infeasible for anyone to do, even when quantum computers come along they won't have enough power to undo the bitcoin chain. Immutable.
Factom anchors into the Bitcoin blockchain, but without all the drama of trying to do so directly, this is it's strength.
NEM uses an entirely new system, Proof-of-Importance:
POI is the algorithm used in NEM to time stamp transactions. A NEM user's importance is determined by how many coins they have and the number of transactions made to and from their wallet.
Make up your own mind.