The only advantage of essence burn is that it can chain endlessly from one initial explosion. So say you kill one, it explodes and now 2 targets next to it are burning, you kill those targets, they in turn explode, and burn additional targets if nearby. But the damage is so small (60% weapon damage over 3 seconds) compared to 50% enemy health (which is huge) that can be buffed to over 100% enemy health on explosion with overawe+soj+flesh is weak.
Invis goes over the mechanics of EP explosion here:
The main point to Essence Burn is if there are large numbers of low-HP enemies, and your weapon damage is high. In this case, Essence Burn can set off a chain reaction, allowing you to farm entire spawns of Fallen, Skeletons or Imps with one cast. This is fairly niche, however.