Leveldb is an awesome key-value store, but it is not really a database. So if you need anything like relationships, queries, transactions, secondary indexed or any of the other features that defines a database, you are pretty much left out in the cold.
Totally, don't get me wrong - I think this is very exciting, and love me some relations. It's just that given all the other data stores mentioned on the page, leveldb is conspicuous in its absence.
This look interesting (also, swift examples!) but I think the biggest problem is how sync the data across devices/users. If this have a good solution for this, I could jump ship from sqlite.