-Capacitors don't really care about temperatures
-Charge and discharge is generally more efficient than in batteries
-Capacitors self-discharge, so depending on what capacitors you use, you'll have to throw your car on the charger after a few days/weeks if you haven't driven it, or add a solar trickle charger
-Capacitors are lighter
-Capacitors can be cheaper
-Capacitors last a lot longer than lead acid batteries
-Capacitors have much less total storage than batteries
-Capacitors can be run to 0v with no negative effects
Mazda Skyactiv cars have a super capacitor bank in them:
http://www2.mazda.com/en/technology/env/i-eloop/
^ Kindof a big deal - some "hybrid" functions in a non-hybrid car. This is a great way to get regenerative braking and stop-start without all of the expensive batteries that need to be replaced after 8-15 years. Alternators are also responsible for ~15% of your total fuel consumption (before you've added aftermarket stuff which consumes electricity) and this heavily supplements the 12v system during city driving.
One problem with lithium batteries in hybrids has been that you can't safely charge/discharge them quickly enough. Having a bank of capacitors could at least partly alleviate that.