Hi Frances,
These are great questions. I am sure they are on the minds of many other readers as well so thanks for raising them.
There are a couple of issues that might be worth clarifying before we get into the specifics: First, although blockchain and distributed ledger are frequently used interchangeably, in reality they are overlapping but not identical comcepts; second, blockchain is a nascent technology that is still developing and there are many variations in its application, so it's often difficult to make categorical statements about it.
There are few existing blockchain applications in finance, with bitcoin being the major exception. Based on what we know about bitcoin, the records are not replicated on every server in the world. There is also a distinction between open (public) and private blockchains, with the latter explicitly only available to people accepted into the network.
Transaction speed is a criticism often leveled against blockchain and it is probably a fair one for many of the applications being tested and in development. There is no evidence that suggests this won't improve over time though, just like any other technology.
Power outage handling is probably in the plus column for blockchain. If some (less than half, to be exact) of the servers storing a particular record are experiencing power outages, people can still access and verify the record replicated on the remaining servers. A centrally administered system can be far more vulnerable.
Warm regards,
Larry