Halogen, xenon, and krypton all refer to the gasses used to fill the bulb.
Light bulbs are usually filled with a mixture of gasses, selected to help retard the evaporation of the filament and to minimize heat loss from the filament. Argon works OK for this, krypton works better, and xenon better still. The better gasses are more expensive, of course. Because flashlight bulbs are so small, it's relatively economical to use pricier gasses like krypton and xenon, so they're pretty common.
Halogen, on the other hand, isn't a particular element or chemical. Halogen bulbs include small amounts of one of the halogen family of elements (usually iodine) in the fill gas. The halogen gas in the bulb can actually bond temporarily with evaporated filament metal, and redeposit the metal back on the filament. This extends the filament life and keeps the bulb's glass free of the filament deposits that make other bulbs turn gray as they age.
There isn't anything mutually exclusive between krypton/xenon and halogen. Some bulbs are both xenon and halogen, or both krypton and halogen.
In any case, the goal of both strategies is the same: to allow the filament to have a reasonably long life when burning at the highest possible temperature, burning more brightly and more efficiently.
There's a lot more detail available on subjects like these at
Don Klipstein's Lighting Info Site. He's got a
page specifically about xenon incandescent flashlight bulbs, and a longer section on incandescent lamps in general, including some
info on halogen bulbs.
As for why Princeton Tec switched technologies as part of a product update, I dunno. The halogen cycle only works in a hot bulb, so halogen bulbs are better off in applications that burn the bulb for several minutes at a time - like indoor lighting, automotive and bicycle lighting, or (I'm guessing) dive lighting. In applications that involve short bursts of light, like walking down a dark trail at night, xenon may be a better choice, because its benefits don't require the bulb to be hot. PT's web site
says the rechargeable Shockwave II uses a halogen bulb; maybe xenon alone couldn't manage the kind of performance (20 watts, 389 lumens claimed) they were shooting for in that version.