The ultracapacitor itself with energy density of 15 Wh/kg (below that of lead acid batteries) are not battery replacements in any way, shape or form, but according to NAWA integration of ultracapacitors into the battery pack could be handy.
The reason is high power output of up to 100 kW/kg (in the future NAWA would like to achieve 500 kW/kg and 25 Wh/kg).
If ultracapacitors would be able to take care of acceleration and regenerative braking power surges, manufacturer would be able to use battery cells that are more energy dense, but can't withstand high power. At least that is the theory, because in many cases batteries do just fine with typical power levels in a car.
Maybe that's why NAWA Technology mentions Formula E – a performance application – in which ultracapacitors would lower weight of the battery by 30%.