DTU is nothing but a blend of CPU, memory and IO. Why do we need a blend when these 3 are pretty clear? Because we want a unit for power. But it is still confusing in many ways. eg: If I simply increase memory will it increase power(DTU)? If yes, how can DTU be a blend? It is a yes. In this memory-increase case, as per the query in the answer given by jyong, DTU will be equivalent to memory(since we increased it). MS has even a pricing model based on this DTU and it raised many questions.
Because of these confusions and questions, MS wanted to bring in another option. We already had some specs in on-premise, why can't we use them? As a result, 'vCore pricing model' was born. In this model we have visibility to RAM and CPU. But not in DTU model.
The counter argument from DTU would be that DTU measures are calibrated using a benchmark that simulates real-world database workload. And that we are not in on-premise anymore ;). Yes it is designed with cloud computing in mind(but is also used in OLTP workloads).
But that is not all. Now that we are entering the pricing model the equation changes. The question now is about money and the bundle(what all features are included). Here DTU has some advantages(the way I see it) but enterprises with many existing licenses would disagree.
We can switch between both when needed so if not sure start with DTU(Basic/Standard/Premium).
How can we know which pricing tier to use? Go to configure menu as given below: (on the right/left you can switch between both)
Even though Vcore is bigger 'machine' and for bigger things, the cost can sometimes be cheaper for enterprise organizations. Here is a proof. DTU costs $147 . But Vcore costs $111. That is because you can commit for 3 years(but still pay monthly) and also because of the license re-use option(enterprises will have on-premise licenses).
It is a bit too much than answering direct question but I am gonna go ahead and make this complete by answering 'how to choose between different options in DTU let alone choosing between DTU and vCore'. This is answered in this beautiful blog and this flowchart explains it all