Since battery chemistry and capacitor chemistry do different things and ahve different voltage ranges, I'm not sure how they could mix them inside one discrete device (like a capacitor can).
Most likely they hybridize the pack as a whole, using batteries for long term discharge, and capacitors for the momentary peaks during charge and discharge, and DC-DC converters to utilize more of the energy of the capacitors (because by themselves only a few percent of the energy you put into them can ever be gotten back out. Capacitor energy range uses a 0V-maxV range, while batteries use a narrow voltage range for all their energy, such as 3v-4.2v, etc.
But I don't know for certain how they're using them. I haven't seen any that give complete actual details.
If you intend to use bare capacitors, of whatever type, as a battery or in conjunction with one, then to actually get all (or most of) the energy out that you put in, you'll need a wide-input-range (preferably 0V to whatever the caps' max voltage is) DC-DC converter as well, one that can handle the currents you need out of them. (since one of the reasons to use caps is to get lower Ri in a pack, for higher momentary discharge rates--if the DC-DC between the caps and the battery/load can't handle those, you lose that ability).
This DC-DC will waste power as heat, so it may need to be cooled, and even if it doesn't itll still take space and cost money.
You can use caps without a DC-DC, but then you only get that small range of useful capacity out of them, whatever the battery's voltage range is. So you need several times as many caps to do the same job, without the DC-DC.
I'd guess that a pure battery pack is going to cost less and be smaller than a capacitor pack or hybrid.