I'm not sure what they cost these days, but ultracaps still cost more overall to design as a portable power supply over a LiIon or NiMH battery, to power a device.
For practical devices, I do own a power screwdriver that uses ultracaps which charges in <=1 minute, and it puts out enough power to run the driver for most any practical job around the house. Given the charge time is short, its very practical in this design, and uses no voltage regulation, the caps are simply tied directly to a DC motor. From near zero volts, to 5+ V, it will charge in 90 seconds, but the torque is pretty useless once below 2.5V, so for practical purposes the caps as useful down to there only. Charging is exponential.
http://www.flashcellscrewdriver.com/The main advantage of ultracaps is that its rated life is not tied to charge cycles like LiIon or NiMH, or aging in 5 years like any Li cell. The expected lifespan of a cap is 10-20 years, due to deterioration of its electrolyte, and its independent of charge cycles, so use it as much as you can. I also use it to power a power vac, it gets about 1 minute of use before it dies, but its so easy to charge up thereafter.
Given this device is out of production since 2007, if you bought a 2nd hand unit, unless the motor burns out or gears strip it should last at least to 2014, to 2021.