Wow, everyone seems to be really worried about dropping their primary light in a cave. In 22 years of diving, I've only ever dropped one cordless light, and that was in the dead of winter when I was wearing 5mm mittens with the light in a soft goodman handle that held the light in a sleeve. The light slipped out of the sleeve and tumbled into deep silt about 60 feet below me in open water. Even though the light was on at the time, I could not see exactly where it went and never did locate it.
However, my point is that that was a once in a couple decades event precipitated by severely unfavorable conditions. I cannot recall anything even like a close call to dropping a light in the cave where I have no gloves in warm water and a dark environment where it will be easy to see where the light goes because if it was in my hand it would also have already been turned on.
Also, if you are side mounting (as several who have mentioned their worry of dropping a light in the cave are prone to do) would you not want to mount your primary on your helmet (in which case the cordless is much simpler)? I see this as akin to why dry cavers now laugh at others who still have head lamps tied to belt mounted battery packs (state of the art 10 or 20 years ago).
Now, as for comfort/weight on the hand, that seems a valid reason for preferring a can light. Brightness would be another, but my experience has been that there are cordless lights that are bright enough and I have seen lights of both types that I consider too bright (that seem to leave me snow blind when another member of the team or myself shine it too close to wherever I am looking). But maybe that's just me.