I hope I won't get lynched for voicing a "minority opinion". I'm still skeptical. DAGs are neat mathematical objects and very trendy at this moment.
The most hyped DAG is IOTA's "Tangle". It doesn't achieve finality, because it cannot, by design. All it can hope for is stochastic convergence toward an ever higher probability ... It's called a Markov chain process. IOTA's argument is that because it targets small transactions (target usage is IoT) a 2€ transaction which has a 99,9% of not being fraudulent is as good as a 100% confirmation
Another rather well-known DAG is the Hedera Hashgraph which is proprietary and closed source. Transaction confirmation is not left to the DAG though (precisely because of finality issues). Instead the DAG is used as meta-gossip layer (they call it "gossip about gossip") to propagate transactions between nodes.
The DAG by design cannot guarantee finality of transactions precisely because it's not a blockchain: there is no "choke point" where the state is being persisted. It's a non-deterministic state machine.
For the rest, I don't quite see how Byteball gets from the DAG to all the applications it advertises. Smart contracts - where's the info about the programming language ? How is execution handled ? Where is the data stored ?
I also don't quite get the concept of "P2P insurance" ... but nevermind, I need to study it in more detail.