The battery that comes with Axim is the standard 1440mAh; an extended battery with something like 3400mAh is indeed available as an option.
According to some reviews of Axim, the standard battery is good for 8-10 hours of normal usage. One review said they played MP3s non-stop for 6 hours 22 minutes before the MP3 player stopped because of not enough power, but Axim still had another 16% on the battery which was good enough for about another full hour of standard usage.
Audio and video will both cut down on how much you can expect from the battery, video much more so than audio. If you are planning on watching full length movies on an airplane from a 1GB Microdrive, I think getting the extended battery would be a good idea. I'll give this a try myself as soon as I get my Axim, which should be... drum roll... the day before Xmas, according to Dell.