[LeonM]

Current battery tech can already deliver enough charge/discharge current to act as a momentary power boost for combustion engines. Many hybrid systems act this way, providing additional acceleration and/or torque filling (i.e. delivering power in between gear-shifts of the ICE). Maybe you could recoup a bit of additional power during hard braking with supercapacitors, but in practice I doubt it's going to make a meaningful difference.

For drones I don't understand why supercapacitors with equal energy density would be beneficial? I don't own a drone, but is charge time an issue?

[maxerickson]

If you can charge a capacitor, your storage battery doesn't have to be designed to meet peak power requirements, rather, average+capacitor charge.

Whether it makes much of a difference who knows, but it may open up different chemistries or whatever.

[JulianMorrison]

Drones probably care more about the output rate than the input rate? If you need a fast recharge you can change out the battery, so that has to be less of an issue. With high output, the drone can go fast, change course in a hurry, carry a lot of weight, or fly into a headwind.