First off, the OP is using the seasons where each player was "39 years old" as listed on basketball-reference.com, which is the '87 season for Kareem and the '03 season for Jordan. This is not entirely accurate. He should be using the 2002 season for Jordan and the 1987 season for Kareem (I know the OP
said he was using the 2002 season, but he quoted Jordan's 2003 numbers). I say this because Jordan was 38 years and 9 months of age to start the 2002 season. Kareem was 38 years and 7 months old to start the 1987 season.
So using the proper seasons, some numbers:
Raw averages:
Jordan: 22.9 pts, 5.7 reb, 5.2 ast, 1.4 stl (41.6% FG)
Kareem: 17.5 pts, 6.7 reb, 2.6 ast, 1.2 blk (56.4% FG)
Per 36 minute averages (since both played < 36 mpg; Kareem significantly so):
Jordan: 23.7 pts, 5.8 reb, 5.3 ast, 1.5 stl (41.6% FG)
Kareem: 20.1 pts, 7.7 reb, 3.0 ast, 1.4 blk (56.4% FG)
Other notes: Jordan was averaging 25.2 pts/6.1 reb/5.2 ast/42% FG prior to the All-Star break that year (he was one of only two players who were putting up 25/6/5 along with TMac), and hurt his knee shortly thereafter. He had also led a team which had won just 19 games the year prior to a 26-21 record and the 6th seed in the East by the All-Star break despite the fact that the Wizards had lost:
- Their leading scorer and second leading rebounder (Juwan Howard (18 pts/7 reb)
- Their fourth leading scorer (Mitch Richmond, 16.2 ppg)
- A 12 pt/7 ast PG (Rod Strickland)
Granted, the latter two players only played 33-37 games in 2001, but they still contributed good production, and the Wizards' roster had significant turnover between the '01 and '02 seasons. Yet despite this, Jordan led them to 7 more wins
by the All-Star break than they had the entire previous season. And he did it while putting up numbers (25+/6+/5+). At basically age 39. It ended up being a +17 games turnaround, and would have been a +24-26 game turnaround had he not gotten injured (that's the pace they were on). It's amazing for a player of any age to have that sort of impact, much less a 39 year old.
Something else to keep in mind is that Jordan was seeing first option defensive pressure while Kareem was not. This does not completely negate the difference in their scoring efficiencies (not nearly, actually, since Jordan was very inefficient that year) but it's something to bear in mind. Another thing to keep in mind is that Jordan did many unprecedented things that season, including becoming the oldest player to ever score 40+ points, oldest to ever score 50+ points, and becoming the only player to ever record back-to-back 40+ point games after age 36 (and he did it twice that season, mind you, including 45/51 back-to-back at age 39). Lastly, Jordan was going up against the "super athletes" of today, not the plodding, floor-bound players of yesteryear. Yes, that last point was a joke.

Ultimately, Kareem was more consistent and efficient. Jordan was great all year (a top 15-20 player that season), but when he was on, he was ON, and when he was off, he was OFF. If I had a good team and needed another piece, I'd probably take Kareem because he was steady and efficient and could provide interior scoring and decent shotblocking. If I needed to take one of them to be "the man" on a worse team, I'd take Jordan without hesitation despite his unusual inefficiency that year, since he proved he could have a large impact on the W/L column on a poor team at an advanced age.