Which are better in a digital camera: Lithium Ion OR AA Alkaline batteries? i.e. how long/how many shots?

Your better cameras use the lithium ion battery. You won't see AA's being used in an DLSR. And not all AA's are created equal. You get what you pay for.

Here comes another long winded explanation. Disposable AA batteries don't only come in alkaline form, and in fact alkaline batteries are not well suited for cameras. The right type of AA battery can provide plenty of life. Recently there have been a number of new type of Lithium disposable batteries. These usually are able to last hundreds of shots with a flash. They are a totally different breed of battery. There is also a type of camera specific battery called a CRV-3 which acts as 2xAA and also last several hundred shots with flash. These are the two modern disposable solutions, both based on non-rechargeable Lithium battery technology. Also a relatively new type of battery is the Lithium Ion rechargeable, these provide a good steady supply of charge and originally started out as batteries for laptops and have found their way into the Tesla Roadster. As rechargeable batteries they have a long service life and provide decent charge to charge endurance, up to 500 shots per charge. However they are expensive, and do not provide very good recycle times for flash. Personally I'd go for the Canon because Samsungs just are not particularly good. As to the battery problems, you needn't worry, Lithium disposables are good and so are NiMH rechargeables.

I have had cameras with both. The Lithium Ion batteries are more expensive but on the whole will hold the charge longer. You do need a spare if you don’t want to be left with a flat battery. If you buy a say, Jessops own this will be cheaper than most camera brands. The AA batteries are more convenient, if you are out & left with flat batteries you can always buy AA ones in most shops as an emergency stop gap. The best AA batteries are rechargeable metal hydride or NiMH. Look along the edge of the battery to see what the capacity is. 2700 should last a while. A number a lot lower will not last any time. Four of these can be bought on line for approx £8-00. If you can find a good battery charger that discharges the batteries before it recharges all the better. But with all rechargeable batteries they can only be recharged a certain number of times before they start not holding their charge. Hope this is of some help

Li-ion designed for the camera is best for power and duration, but it's expensive to have a spare for every camera and mains power might not be available on a long day out. Both my DSLR and compact use Li-ion. If you're going to use AA, then buy a good quality charger (about £40) and decent branded Ni-MH batteries (about £10 for 4). Then have two spare sets of charged batteries with you, just in case. For my flashgun I'm currently using Jessops batteries, but with an Ansmann charger. I probably wouldn't buy a compact that used AA, but that reflects my position as an experienced amateur who doesn't spend long periods away from mains power. Witness Stephen Fry in the recent Last Chance to See TV show when he was in the Amazonian rain forest and couldn't find a mains outlet. There are solutions out there though: Instant Power [1] Ansmann [2]

It's a matter of preference. Some prefer the long-life of rechargeable Lithiums while others prefer the wide availability of AAs. Alkalines are the minimum for disposables with Energizer Lithiums being the best. You'd be amazed at how far they go but still they fall short compared to rechargeables. The only problem with propriety rechargeable batteries is getting a replacement or backup battery which is considerably much harder than disposables. Canon makes better cameras than Samsung but uses up batteries faster. When powered by AA batteries, you can opt out for rechargeable AAs anyway.

You have a couple issues working here; 1. you want a camera that is not an energy hog! 2. Do you want the reliability of Lithium or the convenience of AA? Keep in mind that you are essentially holding a PC with a lens and flash. I personally had a bad experience with Samsung; shutter lag big time. Think about it; how long do you think 2 AA batteries will hold up, especially if you use the flash? That was another issue; cameras that have power issues also take long times to get you to the next shot. The Canon A480, as I recall, is 10MP with a 3.5x zoom and uses 2 AA. I looked at one for my grandson, but felt it looked too "plastic" and went with a Nikon Coolpix, with the same features and for $20 less. I do recommend that you try another Canon model with similar features and a rechargeable Lithium battery. I have the 850 IS and really like it. Check whatever you choose on CNET.com and read user comments. They can be almost as important as the editor's review!

The newer camera will take many more than 40 shots with a set of AA batteries alkaline batteries. But the battery cost will still be more over the life of the camera than if you have the rechargable Lithium Ion Battery. The cost won't be terrible, considering you may get 150-300 shots out of the AA's, but if you take many thousands of pictures, over the life of the camera, the cost will be significant, compared to the cost of the camera.