With the proviso that I haven’t used Datomic in production, thought I’d give you an answer.

Advantages

1. Datalog queries are powerful (more so than non-recursive SQL) and very expressive.
2. Queries can be written with Clojure data structures, and it’s NOT a weak DSL like many SQL libraries that allow you to query with data structures.
3. It’s immutable, so you get the advantages that immutability gives you in Clojure/other languages as well
   a. This also allows you to store, while saving structures, all past facts in your database—this is VERY useful for auditing & more

Disadvantages

1. It can be slow, as Datalog is just going to be slower than equivalent SQL (assuming an equivalent SQL statement can be written).
2. If you are writing a LOT, you could maybe need to worry about the single transactor getting overwhelmed. This seems unlikely for most cases, but it’s something to think about (you could do a sort of shard, though, and probably save yourself; but this isn’t a DB for e.g. storing stock tick data).
3. It’s a bit tricky to get up and running with, and it’s expensive, and the licensing and price makes it difficult to use a hosted instance with it: you’ll need to be dealing with sysadminning this yourself instead of using something like Postgres on Heroku or Mongo at MongoHQ

I’m sure I’m missing some on each side, and though I have 3 listed under disadvantages, I think that the advantages outweigh them in more circumstances where disadvantages don’t preclude its use. Price is probably the one that will prevent its being used in most small projects (that you expect to outlast the 1 year free trial).

Cf. this short post describing Datomic simply for some more information.

Expressivity (c.f. Datalog) and immutability are awesome. It’s SO much fun to work with Dataomic in that regard, and you can tell it’s powerful just by using it a bit.