you can expect around 2 or so hours of regulated output on a CR123 battery on the P1 (more or less depending on the capacity/quality/brand of your battery), and a long tail of dim light once it drops out of regulation. of course, once the battery is done, it's done.
on a rechargeable, you can expect much higher output, but a relatively non-regulated curve, and probably only for about 40-50 minutes before the protection circuit shuts the battery down (assuming you are using protected batteries), depending on the mAh rating of your RCR123 cell. of course once the circuit shuts the battery down, you get no light and the battery will be shut down until you pop it into the dsd charger to reset the circuit. short runtime, but you get more brightness, and of course, you can recharge these batteries as you want (and carry a spare too for more runtime, just as you carry a spare non-rechargeable).
this graph by Chevrofreak shows it pretty nicely -->
http://candlepowerforums.com/vb/showthread.php?t=130671
Edit: considering lithiums have a long shelf life, i'd buy maybe 4 RCR123s and use them for everyday use, and save the primaries for extended journeys (camping, travel, etc.), spares/backups, and emergencies.
