More advanced electronic systems are usually also more efficient, which means better battery duration, and some cameras can take over 400 shots on a single charge, but it's still worth taking a look at the capacity of the battery. Most compact digital cameras have proprietary Lithium-ion rechargeable batteries, which work better in cold conditions and don't suffer from the "memory effect" that was a major problem with older types of rechargeables. The downside of Li-ion batteries is that spares and replacements can be very expensive, and if you run out of power while out shooting there's nothing you can do about it until you get home to your mains charger.
Some cameras, particularly larger compacts, run on AA batteries. While they are bigger and heavier than Li-ion cells, they do have a couple of advantages. High-capacity rechargeable Nickle-metal hydride (Ni-MH) AA batteries are relatively cheap and very efficient, and while they don't perform as well in the cold as Li-ion cells, it's easy to swap out a cold set for a warm set from your pocket. Also, AA batteries are available almost everywhere in the world, so if you run out of juice on a day out you can just pop to the corner shop and get a new set.
When you're considering your budget for a new camera, don't forget to factor in a enough memory cards for your needs. Fortunately the price of these has dropped faster than a particularly aerodynamic stone, and you can now get top-quality one-gigabyte cards for under £10.
The vast majority of digital compact cameras use Secure Digital (SD) or SD High Capacity (SDHC) cards, but not all of them. Sony compact cameras use Sony's own Memory Stick or Pro Duo cards, which tend to be a bit more expensive. Olympus cameras use another format called xD-Picture cards which are more expensive still, and can be harder to find, although some recent Olympus compacts come with an adapter that lets them use the MicroSD cards that are used in some mobile phones.
Although entry-level and even some mid-range DSLRs use SD cards, the top professional cameras use the larger CompactFlash (CF) cards. These come in two sizes, the thinner Type I and the thicker (and much less common) Type II. Fortunately most cameras that use CF cards can accept both types.
Whatever type of card your camera takes, it's always a good idea to buy from a leading reputable brand, even if it means paying a little more. Cheap memory can be slow, and worse unreliable. Don't trust your pictures to something that might let you down.