I would take Kobe in a heart beat. This isn't even a contest. It all comes down to basketball skills. Kobe can shoot, and I mean really shoot. Lebron can't.
Opponents play Lebron with a defensive strategy to try and make him shoot from the outside, because he is not a great shooter. Most likely he will miss and they can get the rebound. Lebron's entire game is based on his size and athletic ability. He drives to the hoop with the intention of getting fouled. Watch him. He doesn't even try to make the shot half the time. He only wants to get to the free throw line.
Kobe cannot be stopped with any strategy other than double and triple teaming him which leaves teammates wide open for easy points. When Kobe drives to the hoop, he is going in to score. If he gets fouled, it is a bonus for him.
Kobe can shoot long range as well as anyone who ever played. He can drive to the hoop and score as well as anyone who ever played. He can handle the ball very well and pass very well.
It could be argued that Lebron is a better passer than Kobe, but Lebron is not a better ball handler. If he is a better passer, it isn't by much.
So, Kobe has the edge over Lebron on offense.
Any coach will tell you a great offensive player is no good if they can't play defense. Kobe is a better defender than Lebron.
Again, Lebron uses his size and strength well, but Kobe defends smarter than Lebron. He is quicker than Lebron and, as a result of those two factors, is a much more dangerous defender.
Just the other night, Kobe stealthily slithered in behind Yao Ming and blocked a dunk attempt by the 7 foot 6 monster. How many smaller players would you see doing that? Not many.
Lebron takes advantage of his team's good defensive plays. He gets a lot of weak side blocks and loose ball steals that were half caused by his teammates. Kobe is more often the reason for the loose balls as he is actually the one disrupting the ball handler.
If Kobe played Lebron one on one, he would win 9 out of 10 games.