I saw a video on youtube recently where someone had replaced his car battery with a couple of super capacitors. Car started perfectly, so some of these super capacitors can definately provide quite a bit of current.
There are different grades with different internal resistances, but since the electrodes are finely divided carbon, internal resistances are much higher than electrolytics - less sparking, think of them more like batteries(*) than capacitors!
However the energy storage is much much higher than electrolytics so that a few cycles of charging up fully and then shorting out will raise the temperature considerably - probably reducing device lifetime too!
(*) low capacity batteries with awful voltage regulation (but high current charge/discharge and wonderful deep-cycle lifetimes)