Same question about "luck" then: should just one or both chars have it?
It is the
average luck that determines drops.
So beefing up the luck of one character is still better than no-one's, but less good than beefing up both's.
How so? If I have two party members with 5 luck each, or one party member with 10 and another with 1 luck, it still works out to 5. For what it's worth, I would suggest giving all permanent stat modifiers you encounter to your PC, even if this provides an uneven distribution of stat points in such areas as luck. My point being, if for some reason any party member leaves you, you still want to have the bulk of those points where they count the most--on your own character.