OP was based on playoffs, not regular season.
Okay I'll look for playoffs for the seasons they were both in the playoffs.
05-06:
Kobe
23 points (7 games) 44% FG. Last minute FG 44%
LeBron
55 points (13 games) 50% FG. Last minute FG 43%
06-07:
Kobe
6 points (5 games) 2/3 FG. Last minute 1/1 FG
LeBron
58 points (20 games) 53% FG. Last minute FG 62%
07-08:
Kobe
51 points (21 games) 48% FG. Last minute FG 40%
LeBron
21 points (13 games) 26% FG. Last minute FG 10%
08-09:
Kobe
47 points (23 games) 41% FG. Last minute FG 33%
LeBron
31 points (14 games) 53% FG. Last minute FG 38%
09-10:
Kobe
47 points (23 games) 39% FG. Last minute FG 44%
LeBron
16 points (11 games) 71% FG. Last minute FG 2/2
10-11:
Kobe
7 points (10 games) 25% FG. Last minute FG 1/3
LeBron
43 points (21 games) 40% FG. Last minute FG 50%
11-12:
Kobe
29 points (12 games) 30% FG. Last minute FG 27%
LeBron
46 points (23 games) 37% FG. Last minute FG 43%
Overall:
Kobe
62/153 41% FG. Last minute 20/53 38% FG
LeBron
80/180 44% FG. Last minute 24/55 FG 44% FG
Obviously that's not including LeBron's long-ass playoff runs since 2012, and not including Kobe's three-peat but during their crossover period of playoff activity LeBron has clearly been more efficient in these metrics, and obviously being better in the regular season too.