Okay. I'll attempt to break it down.
P1 -- original Luxeon version. Plenty bright for most people, the absolute smallest CR123 light from Fenix. Simple on/off, only one output level.
P1D -- digital series Fenix, with 3 output levels and SOS and strobe. Uses a Luxeon LED. Larger than the P1, but still pretty reasonably sized. (Still pretty tiny!)
P1D-CE -- digital series Fenix, same as above, but with a Cree LED. Cree LED's are twice as bright in this application as a Luxeon, with no drop in runtime. If the extra cost doesn't matter to you, there is no disadvantage to the -CE models.
P1-CE -- updated version of the P1. One output level (simple on/off), uses a Cree LED for twice the brightness. Runs slightly longer than the original P1 but not by a significant margin (5-15 minutes). Ever so slightly larger than the P1 (new brass heatsink), with a modified design but aside from brightness functionally the same as the P1.
Also note, Cree versions are about twice as bright as the Luxeon models, run for about the same amount of time if not slightly more, and do not get as warm.
There's also special editions that use orange peel reflectors that make the beam smoother and "more pleasing to the eye," as well as (slightly) better binned LEDs (hand-picked, essentially). They are a bit more money but some believe they are worth it.