There's another aspect, unforgeability. The interesting thing about the blockchain is that it is a very hard to forge data-set, by design. You can take a proof of work blockchain and look at the hashes of the blocks in it, and based on the number of 0's in each block (the difficulty), you can know how much energy (and cost) went into mining that block.

So if there's a danger of forgery, or you have an interest in security, a blockchain with proof of work provides a really trustworthy way to know you're getting authentic data, because you can look at the chain, and know things like it would cost about 100,000,000 to forge this full history, and 1,000,000 to forge to last block.