Essentially the same printers, they differ largely in terms of the resolution they offer. The 310 does 300x300dpi, the 320 gives you 600x300 and the 340 offers 600x600. All in a nice, slim, black casing. The battery allegedly lasts up to 4 hours, but I'm inclined to take that figure with a grain of salt. Like PowerBooks and PC notebooks, they may travel rough and they're more likely to get dusty.
Portable printers are harder to work on that their desktop inkjet cousins.
I tend to recommend the used Apple StyleWriters to people who want portable printing on a budget. Both are still in production and both are readily available on the used market. Depending on whether you're making a direct connection to the printer or through a network, you'll need either an ethernet crossover cable, or a standard cat5 ethernet cable that goes through a hub. And, if not, you can buy these at a supermarket even. APU's better and more fully-featured.