Super caps are lower voltage (1.2V or so each), so need to be wired in series and parallel combinations to be able to get accessible voltage from them. You will generally need a buck boost converter on the output side to adjust the voltage dependent on the charge left in the super capacitors.
Compared to a Lion battery where you can get a much linear voltage over a smaller range in relation to charge, so generally a buck converter will suffice.
So as a replacement for battery not really, there are too many issues with them. As a complement to a battery use. Do you want to the device to remain powered after power lose? for a reasonable time to change batteries and the like? then super caps may be the answer.