Afaik, Postgres flavored Aurora has a single master for writes and doesn't allow horizontally scaling writes[1]. I believe reads can scale by bringing up multiple read replicas. Cockroach DB is "distributed SQL" so writes are also scaled across multiple nodes.

You can see some details about how this affects write perf in this blog by another distributed SQL database which compares the three databases (YugabyteDB, Aurora and CockroachDB) - https://blog.yugabyte.com/comparing-distributed-sql-performa...

[1] There is also multi-master Aurora (but based on https://docs.aws.amazon.com/AmazonRDS/latest/AuroraUserGuide... that only supports 2 read-write masters and has other limitations).

Being able to run it yourself is a big thing. You can also run one cluster across multiple cloud platforms (AWS, GCP, Azure), so there is no vendor lock in apart from obviously the database choice, and you aren’t tied to the availability of any one platform.