Kinda funny this got posted. I was actually thinking about this on my drive to work this morning. Full disclosure, I lived in Denver when Melo was drafted and was really happy to get him on the Nuggets. So I've seen quite a bit of Melo play.
As far as simply scoring talent goes, I have to give the edge to Carmello. Mostly because he is a better shooter than LeBron. But like others have said, he is a selfish player and really only cares about points. I remember countless George Karl interviews in which he criticized Melo for not rebounding or doing the other little things it takes to win.
LeBron not only does the little things, he's probably to best to ever do them. To me the best way to measure a player is by how much better he makes the players around him play. JR's knucklehead fouls aside, he seems like a more team-oriented player with LeBron than with Melo. And anyone that can get JR to buy in to the team concept wins this argument hands down.
So yeah, LeBron. And it's not close.