The yellow Photon II runs for a long time for the simple reason that it's rather dim and doesn't use much power. The white one (when run with two 2016 cells) is a lot brighter and doesn't last as long. You can run the white one on a single 2032 (twice as thick as a 2016) and it will also last for a very long time (and be dim). The Photon Freedom is variable-powered, so you can set the brightness you want. If you set it down low, it doesn't use much power and lasts a long time. You can set it high if you need more light. The Photon III is similar, but just three levels (hi/med/lo) instead of continuous adjustment. So, if you have a white Photon III or Freedom, you can select the power level and have long runtime AND white light AND brightness when you need it. At that point, there's no advantage to the yellow version unless you like yellow light for some reason.

The main problems with all the Photons is 1) they're sort of expensive (especially the III and Freedom) and 2) they have momentary pressure switches, so if they're squished inside some kind of compressible pak, they can turn on by accident. The III and Freedom do let you change batteries with no tools (the II requires a #00 Phillips screwdriver) and spare coin cells are even more compact than the little lights are.

Personally I like the $1.00 Countycomm lights which are sort of like cheap Photon II knockoffs with no momentary function (just a constant-on slide switch). If you tape the switch down for storage, it pretty much can't switch on by accident. And they're cheap enough that you can stash them all over the place.