I'm in the "It's LeBron, and it's not close" camp. I believe Kobe is an outstanding player, and that he has been a top-5 player in the NBA for about a decade. He's been top-3 for much of his prime, but for the most part I think some combo of Shaq, Duncan, Garnett, and LeBron have been better than him pretty much every year of his career. These days, Wade has definitely entered the discussion as well.
So why is Kobe so often considered "the best player on the planet" or so often in the "could he be as good as Jordan" conversations whereas someone like Duncan is rarely mentioned? IMO, it's because Kobe's playing style is the most similar to Jordan's, and many consider Jordan the GOAT, so by transitive reasoning the player who plays most like Jordan must be the current best player.
I disagree with that. Kobe's scoring is outstanding, and he is definitely one of the better clutch players in the NBA. But I think "clutch scoring" has become almost overrated...as Roy points out, Carmelo Anthony is probably the best clutch scorer in the NBA. But there's no way on earth he's even top-10 among players overall.
To me, it's about overall impact. How many points are you worth to your team, and how much are you able to prevent the other team. And to me, LeBron has a much bigger impact than Kobe does right now. People mention "size" almost in passing, or in some cases almost as a negative against LeBron (?!), but in reality that is a huge part of the difference. LeBron's size makes him next-to-unstoppable on offense, to a degree that Kobe can't consistently match despite his vast skill. LeBron's size allows him to be a monster defensively as well, not just taking out his own man (like he did against Pierce) but also allowing him to protect the rim, patrol the paint, and dominate on the glass. Kobe's upside as a defender is as a lock-down guy, and even that he only can do in spurts without affecting his offense. Kobe's defensive impact is IMO one of the most overrated portions of his game.
So yeah, LeBron or Kobe? LeBron fairly easily.