Really there is no debate between Lebron and Kobe, but Shaq gave him 3 rings so therein lies the misconception.
"Playoff Games
Game 7 of a Playoff Series
Kobe 22.2ppg on 38.9% FG with 8.0rpg and 5.0apg (6 games)
LeBron *34.0ppg on 46.5% FG with 8.1rpg and 3.5 APG (4 games) (*NBA Record)
LeBron is clearly the better player when it pertains to game 7s
Elimination Games
Kobe 21.5 ppg on 41.4% FG with 5.8rpg and 3.5apg (19 games)
LeBron 31.5 ppg on 46% FG with 10.0rpg and 6.5apg (12 games)
LeBron is also clearly the better player when facing elimination.
I have deliberately left out the two players records in these games because whether a team wins or loses is a team accomplishment. Basketball is a team game and therefore its foolish to attribute a loss to just one player alone.
Game 7 of their most recent NBA Finals
Kobe in game 7 of the 2010 NBA Finals: 23 points, 6-for-24 shooting (0 for 6 from 3pt range), 25% FG, 15 rebounds, 2 assists, 1 steal, 4 turnovers
LeBron in game 7 of the 2013 NBA Finals: 37 points, 12 for 23 shooting (5 for 7 from 3pt range), 52% FG, 12 rebounds, 4 assists, 2 steals and 2 turnovers."