It depends what you're aiming for.

If you only lightly use your camera, you're going to want batteries with a very low discharge rate. The lowest discharge rate will be with Lithium based AAs, but they are very expensive. They even tend to cost about $2 per battery in bulk. They will also tend to last longer than anything but a freshly charged set of NIMH batteries, of which almost all will die pretty quickly even without any usage at all.

Lithium AAs:
http://www.batteryspace.com/index.asp?PageAction=VIEWPROD&ProdID=3860

Eneloop:
http://www.eneloop.info/
The best rechargable batteries for low use situations are the aforementioned Sanyo Eneloops. They have significantly lower capacity than the best normal NIMH batteries (2000MAH versus 2600-2900), but will not die over time.

If you use your camera a lot, you need plain old NIMH batteries. A higher MAH rating is better. They will lose a lot of their charge in the first month or so, and lose the rest of it somewhat more slowly, so usually what people do with these is charge them every time before they use them if they aren't being used on a regular basis. They can have battery life that's 30-50% better than the Eneloops and approaches and maybe passes the best AA lithium batteries, but the discharge may be a problem for you.

Plain old alkalines frankly suck for high drain devices like digital cameras. While they actually do have more power than many NIMH batteries, they drain somewhat differently - power goes down gradually, and they work a lot better with devices that only need a little bit of power, not ones that need a lot of power. They work fine in a pinch, but don't represent anything resembling the best batteries for use in a digital camera.

Cameras with their own batteries usually use Lithium rechargable batteries, which have more power relative to the size they are - the smallest digicams can't fit AAs, so they will have a little squareish Lion battery. These will tend to have better life than slightly larger cameras that may use 2 AA batteries. Still larger cameras may use 4 AAs, or a larger Lion battery, and there will be more variance as to what gets better battery life if you're making that comparison.

My little P&S cameras (A Canon A710IS and A470) both use 2 AA batteries. They work fine with Alkalines if I need something to run out with *now*, but to give you an example of how poorly they can do, I once took the A710 out with a pair of alkalines in the cold at night, with a tripod, and took a few long exposure shots. I got about 12-13 photos in before the batteries died. When they warmed up later they were OK for a few more shots, but not much.

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