A blockchain provides a guarantee of (statisical eventual) write availability, since anyone can mine new blocks (eventually). A verifiable log only accepts new entries from a limited, generally closed set of writers (usually just one), and you can only add new entries by going through one of those writers. (Blockchains also tend to have better read availability due to being more widely distributed, but there's no reason why you couldn't destribute a verifiable log that widely, it just tends not to happen in practice.)

This makes a verifiable log unsuitable for financial purposes since a adversary with lead pipe capabilities (or corrupt judge capabilities as the case may be) can block undesirable transactions at a single (or few) point of failure, whereas against a blockchain they'd have to target anyone with significant compute capacity.

On the other hand, verifiable logs don't need proof of work/stake/etc to limit hostile forking, so if the log is describing things rather than acting a ground source of truth (so you can just ignore it if it starts refusing writes), it's much more efficient than a blockchain.