If you check out Eveready's web site you can get the ratings of their batteries. Typical C Cells that the Light Cannon uses have about 9 Ahr (9000 MAH). So they will last longer in the light, but of course, can't be recharged. Rechargable Alkalines exist, but they can't be recharged back to 9000 mAh - far less.
NiMH give the best characteristics - high energy density and recharability - for the cheapest source of battery power.
Alkalines are the best if you need a light that will be left on the shelf or in the trunk of your car and used months later since alkalines have about a 10 year shelf life, whereas NiMH and NiCD lose about 10% of their charge per month.
NiCD will give the most current of all, NiMH is close and Alkaline are not that good for really high drain applications (the LC will draw a bit more than 1 amp so it's not really a high drain).
NiCD have a memory effect, but if you drain the batteries completely once every 5-10 charges the effect is not that bad.
Note that the NiMH C size batteries you get at Radio Shack or Walmart are of low rating - typically 2200 mAhr. Check out e-bay for good deals on higher rated batteries.