AA NIMH would be rechargeable, saving you some money in the long run. But they'd still have relatively short life per charge, so if you were shooting a lot...on vacation, for example...you would want to have at least one set of spares in your pocket, if not more. There's nothing worse than running out of power midday and not having backups.
I do not have personal experience with any of the three cameras. But physics plays a major part in what these kinds of cameras are capable of providing. They all share similarly sized sensors and lenses, and those are the two things that determine image quality more than anything else. Because they are so similar, the difference in quality is negligible. Same with the flash; they all have flashes that have approximately the same power, and will produce what most people would describe as adequate to poor (unnatural looking). The zoom range between the three is again similar; the quality will be good in the center, and softer towards the edges...normal for any camera.
The only way to get easily seen better image quality is to choose a camera with a bigger sensor and/or a wider aperture lens. But that requires money.