Ball handler you can argue (I'd go Kobe), but Lebron is a way better penetrator than Kobe ever was. Higher frequency, higher success rate, better facilitator and scorer off the drive. It's what made Lebron Lebron. Kobe mastered every trick in the book and could create some space anywhere on the court, but penetrating towards the basket? This isn't close.
Shooting? Kobe was better at shooting bad shots and much better at FTs. Lebron takes smarter shots and shoots far more efficiently. And because defenders are afraid to play him tight on the perimeter (because he's a better penetrator) he gets more open 3's than Kobe did and shoots them better.
Defending the perimeter. In their primes Kobe was better. Both are lulzy in their later years.
Ability to lead? Both guys are perpetual divas who always seem close to having their team implode. Meh.
Mental toughness? I guess Kobe. But people who point to Bern cramps are being ridiculous.
Clutchness? Kobe isn't really a great clutch shooter. He just took so many clutch shots you can fill a long highlight reel of his makes. But by the numbers he's nothing special in this area. You can do the same with Lebron, though his failures are far more famous than Kobe's were. I still go Kobe, but I think this is an overrated category for him.
This leaves out everything else which almost all points Lebron, except team accomplishments.