The big improvement is the removal of the need to trust some 3rd party but also to add the precision and complexity of computer language to some domain. For example health care data, a block chain system would make one standard for how the records are stored, it would make it so the data in encrypted by the patient and they alone could grant access. When a new provider wants access there is one standard way that is automated and secure. None of which is dependent on a 3rd party who can be compromised or become corrupt and no longer act in good faith. Obviously there is a lot of details here dependent on making the block chain work flawlessly.
Imo block chains have 2 core issues to over come in order to really solve problems. First is being constructed so that they are bug free. Software is not a mature enough discipline for that as of yet. Second, is what happens when you loose you key or it gets stolen. If someone steals you Bitcoin private key, you can’t get them back after they transfer them out. Or if you just loose the key your up a creek. What is required is a way to prove you are you to the system that can’t be stolen and can’t be lost. That is a far harder question.