LA would be better since LeBron is more physical and can force his way inside better. Kobe could do most of what LeBron does, but I don't think his body could take the pounding going inside. People don't like to take a charge from LeBron but Kobe isn't nearly as physically imposing.
Also LA has a better surrounding cast. Gasol is much better than Z, and Bynum or Odom much better that Varajo.
I don't know where you get this utter BS about nobody wanting to take a charge on LeBron, people take charges from Dwight and Shaq, you think LeBron is any more imposing? SILLY!
IMO LeBron would be worse in LA because the team is not designed for his strengths. The Lakers do not have shooters to space the floor, as evident in the last two series, so LeBron would find the paint shut down to his drives. He would have to rely on his outside shooting and obviously Kobe is superior in that department. The way the Lakers are built you need a solid mid range game.
Kobe would not do as well with the Cav either because the Cavs don't have an inside presence and they would be strictly a perimeter team since Kobe is less of a slasher now. There would be nobody for Kobe to play inside/out or vice versa with so he would probably be extreemly perimeter oriented. LeBron offsets their outside shooting big men by scoring in the paint a lot so he's better off there.
So switching their entire teams does not do them much good but moving just one or two key pieces from the Lakers to the Cavs would make LeBron a lock for a ring BUT the reverse it NOT true, moving some pieces from the Cavs to the Lakers would not help Kobe at all. The problem is the Lakers have the talent but no desire and Cavs have all the desire but not the talent. Put the Cavs desire into the Lakers talent and they cake walk to a ring, put the Lakers talent into the Cavs desire and they cake walk to a ring as well.