the IOTA tangle is an innovation on the blockchain. Where the blockchain is a Linked List data structure that is optimized for forward only reading and a single timeline of transactions, the Tangle is a more sophisticated data structure. The Directed Acyclic Graph allows for multiple parallel ledgers that fork like a tree and then merge back to reconcile. (very similar to git branches). The advantages and complexities of the tangle are obvious to those who have studied data structures and algorithms. The blockchain is one source of truth for all actors in that network's universe, it is copied in full and must be synced in full (expensive and time consuming). The downside is that if I want to buy an ice cream from Mr Softee with Bitcoin (blockchain) that transaction will not be settled until all the previously initiated transactions (such as JPMs $350MM purchase of BTC from the exchange) have been settled. This process is slow but the state of the entire universe is more deterministic. When I ask the question, "what is the last completed transaction" I only need to read the last node on the blockchain (and wait for a few blocks to make sure it wasn't reversed?) . On the other hand, the tangle allows me to initiate and finalize the ice cream purchase instantly in a near ACIDic way, our local transaction does not need to be agreed on by the entire universe, just us and perhaps a few witnesses, before it is complete and permanent. This is a much better model for point of sale. This is how IOTA (where the IOT stands for Internet Of Things) is able to keep transactions fee-less and is positioning itself to be the network and token for devices that need frequent real time communication.
If the trade-offs here feel similar to the trade-offs between relational databases and no-sql databases, it's because they are. At the end of the day, all of these technologies are built on top of the same well studied data structures and the innovation is happening by applying them to new industries.