Generally speaking you should get much better battery life/useage characteristics from a camera manufacturers own design of rechargeable battery(ies) than from using AA or AAA etc rechargeables - whether they be NiMh or Lion. One thing is for certain alkalines are really only for emergency use!
There have been many digital cameras in the past that have had a reputation for eating batteries in a very short time - ie couple of days when the camera is off and hours or minutes when the camera is on. This has been due to any or all of the following - excessive use of the lcd screen to revue images, not letting the lcd switch itself off after 30 seconds of inactivity and a host of other user issues, but the biggest one of all - there is a short in the camera. Its not located anywhere that will stop the camera from working but just sitting there warming a chip etc nicely.
Why would anyone want a dslr instead of a decent point and shoot. Loads of reasons but optical quality is quite a big one. Some compact cameras have truly superb quality optics, others - that you may have hoped were also superb can leave a lot to be desired, but the thing is that most people don't really push the optics of their compacts. They don't tend to print large images from them, much as with point and shoot film cameras, they only tend to print at standard 'enprint' size of 6 x 4 inches and some don't even get past the computer screen or lcd photo frame where sub 2MB images are more than adequate. If the image looks dodgy as a 6x4, and its not operator induced, then you really do have a duff camera! If you were to shoot the same scene with a compact and a decent dslr side by side at the same time you should see the difference in quality. Shooting 'all manual' on a compact can be at best a PITA, especially focus whereas on a dslr with manual focus and through the lens viewing its a doddle. I am not entirely convinced about lcd eyepieces.
Compacts do have their advantages - minimal dust on sensor issues, weight, size, cost and for probably the majority of people a GOOD compact camera will do everything they need - if only they could remember how to get through all of the sub menus to set it up ;o)
Dudley