Unfortunately, nothing is ever simple; comparing Spanner and CockroachDB is comparing apples to oranges. Two years ago, we wrote an article that details exactly how the differences matter in terms of a Zanzibar implementation[0], but I can give as short of a summary as possible: Spanner is linearizable and CockroachDB only guarantees external consistency for transactions that share rows. The post outlines how we workaround this and we've also more recently talked about how we've managed to scale that to 1M requests per second[1]. Our team focuses a lot on CockroachDB because we offer a permission systems that can span not only regions within a single cloud, but across various cloud providers. However, if you're all in on GCP, SpiceDB itself supports Cloud Spanner (which we also use in production for our GCP-only customers).
[0]: https://authzed.com/blog/prevent-newenemy-cockroachdb
[1]: https://authzed.com/blog/maximizing-cockroachdb-performance