It definitely looks like DAG-based currencies are the future - at least for currencies aiming to be value transfers. Blockchain can't compete with them (on scalability, speed, transaction fees, etc), even with DAGs as they are today. Check out this DAG coin comparison (RaiBlocks, IOTA, Byteball) - they are way ahead of the Blockchain in many ways.

That being said, DAG-based coins are nowhere near as proven out as blockchains, so they may go through some growing pains.