I only have a passing familiarity with BitD so won’t try to comment on clocks. I do love Dramatic Tasks, however, and they are a mechanism I probably use as often as combat when GMing SWADE.
The strength of Dramatic Tasks, for me, is that they do put mechanical weight into what the characters are attempting. And those mechanics integrate well with the wider rules and character Edges etc. An overall scene is defined, and the GM decides how many rounds, how many successes are required, what kind of time those rounds represent and so on. They can be completely separate from combat or run in parallel with it to represent scenarios like “can the warriors hold off the enemy horde while the mages cast the ritual” etc.
The initiative system is used well and adds to the drama in a few ways in my experience. First, it shakes things up, especially when there are ‘bad actors’ in the mix, too. Second, you can draw a Joker which is a big bonus, or a Club which represents a complication. Complications are cool as they mean even the GM doesn’t know exactly how the scene will play out and the possibility of immediate failure adds huge tension. Finally, it connects with all the Edges based on the initiative system, and it is cool that the players get the benefit of these things they have spent their advances on.
The generation of successes, and how the players approach this, really drives the scene narrative and gives them real agency. As GM you need to make sure they they aren’t just spamming their best skill in a boring way, but otherwise pretty much anything can go.
The great thing about Savage Worlds IMO is that it provides a range of tools, and they scale nicely from a single dice roll, to a handful of rolls or up to a detailed scene with multiple rounds of meaningful action. That range of scale can apply to both combat and non-combat scenes which is more mechanical support than most games provide in my experience.
You don’t have to use any of them and certainly don’t use them at a time when you feel it will be counter productive to the feel of the game. But they are there when you do want them.