Hod @ Couchbase. Couchbase Mobile has had sync for a long time. It's used in serious, large scale deployments. (Check out the video from Ryan Air if you want to see a really cool example of how they were able to improve their app with it.) Couchbase is a document oriented database storing JSON and blobs. (I'm not a Realm expert, so I won't attempt to compare sync solutions.)
(Adam from Realm) Realm is an ACID compliant object database. Compared to Couchbase it is much more performant and memory efficient. In terms of data sync, Realm works by transferring the compressed changes from the transaction log (so just the diffs and capturing the semantic intent of the action) and automatically resolving conflicts using operational transformation. This approaches leads to extremely low latency enabling realtime collaboration functionality. This is quite different than Couchbase which is sending the entire object, requiring the developer to manually resolve conflicts.
I honestly haven't tried Couchbase mobile or CloudantSync. I got a few questions about Couchbase when I was teaching my last class on RN, and I've been meaning to try it. It sounds powerful and popular.