Because Bird started succumbing to injuries beginning with the 88-89 season, we have 4 informative seasons (from 84-85 to 87-88) and 2 playoffs encounters (86 and 87) to use in this H2H comparison.
84-85 Season:
11/15/84-
Jordan: 27/2/2 (12/24. 3/3)
Bird: 14/17/3 (6/17, 2/2)
Celtics win.
12/22/84-
Jordan: 32/12/8 (12/18, 8/8)
Bird: 10/7/4 (3/14, 4/4) - injured; McHale and Johnson DNP
Bulls win.
1/9/85-
Jordan: 36/6/6 (12/24, 12/13)
Bird: 28/11/4/3/3 (9/21, 10/10)
Celtics win.
2/5/85-
Jordan: 41/12/7 (14/25, 13/14)
Bird: 27/9/7 (9/21, 8/8)
Celtics win.
2/22/85-
Jordan: 26/4/7 (8/18, 10/12)
Bird: 34/8/5 (16/28, 0/0)
Celtics win.
3/6/85-
Jordan: 33/7/3 (13/28, 7/7)
Bird: 25/9/10 (11/24, 2/2)
Bulls win.
Cumulative Stats-
Jordan: 32.5/7.2/5.5 (52%)
Bird: 23.0/10.2/5.5 (44%)
In his rookie season Jordan actually had his best performances compared to Larry and really played well.
85-86 Season:
3/21/86-
Jordan: 20/2/1 (7/16, 6/7) - in 16 min
Bird: 32/6/8 (11/18, 8/8)
Celtics win.
In 85-86, MJ missed 5/6 of the regular season games against Boston due to injury and the one that he played it was off the bench with limited minutes.
85-86 Playoffs:
Game 1-
Jordan: 49/4/2 (18/36, 13/15)
Bird: 30/6/8 (9/13, 10/13)
Game 2-
Jordan: 63/5/6 (22/41, 19/21)
Bird: 36/12/8 (14/27, 6/7)
Game 3-
Jordan: 19/10/9 (8/18, 2/3)
Bird: 19/6/8 (5/13, 9/10)
Cumulative Stats-
Bird: 28.3/8.0/8.0 (53%)
Jordan: 43.7/6.3/5.7 (50.5%)
Celtics win 3-0.
Jordan put up better numbers and had that legendary 63 point Game 2 in a 2OT loss. Funny enough, no one mentions Game 3 in Chicago where Jordan choked, scoring only 19 points on 8-18 shooting with 5 turnovers. It has been said that Boston coach KC Jones decided to let Jordan get his in Game 1 & 2 while shutting down everyone else. Seeing how close the first 2 games were and the fact that MJ could go for 60+ points if "you let him get his", KC decided to reverse the strategy and lock down on MJ in Game 3 which supposedly destroyed his offensive rhythm.
86-87 Season:
11/14/86-
Bird: 37/10/5 (52%)
Jordan: 48/5/1 (51.5%)
Celtics win.
01/02/87-
Bird: 37/8/9 (61.1%)
Jordan: 34/8/3 (41.9%)
Celtics win. Bird easily outplays Jordan.
27/01/87-
Bird: 24/14/3 (39%)
Jordan: 30/5/6 (38%)
Celtics win.
28/01/87-
Bird: 26/5/9 (65%)
Jordan: 27/4/4 (48%)
Celtics win. Bird wins match-up.
27/03/87-
Bird: 41/7/7 (58.6%)
Jordan: 22/7/7 (39.1%)
Celtics win. Bird easily wins match-up.
17/04/87-
Bird: 38/8/7 (59%)
Jordan: 17/4/8 (33%)
Celtics win. Bird easily wins match-up.
Cumulative Stats-
Bird: 33.7/8.8/6.5 (56%)
Jordan: 29.7/5.5/4.8 (43%)
Bird really pistol-whipped MJ this season. Outplayed him in arguably every game and Celtics won 6-0.
87 Playoffs:
Game 1-
Jordan: 35/6/7 (12/25, 11/11)
Bird: 17/9/13 (4/7, 7/7)
Game 2-
Jordan: 42/4/4 (14/29, 12/14)
Bird: 29/7/8 (9/17, 11/13)
Game 3-
Jordan: 30/11/7 (9/30, 12/14)
Bird: 32/14/6 (11/21, 10/11)
Cumulative Stats-
Bird: 26.0/10.0/9.0 (53%)
Jordan: 35.7/7.0/6.0 (41.7%)
Celtics win 3-0.
Bird again outplayed MJ in this postseason. Jordan scored more in volume but on poor efficiency and again saved his worst game for the pivotal Game 3 in Chicago. With the Bulls up 7 with 11 min left, Jordan went 0-8 from the field the rest of the way and 9-30 overall. Bird scored 15 points in the final stanza, dominating the Bulls and sweeping the series.
87-88 Season:
12/01/88-
Bird: 38/9/8 (58%)
Jordan: 42/4/6 (53%)
Celtics win. Bird wins match-up.
18/03/88-
Bird: 19/10/6 (42%)
Jordan: 50/5/9 (59%)
Bulls win. Jordan finally wins head to head and it's the only time he really outplayed Bird in these 2 seasons.
20/03/88-
Bird: 33/7/8 (67%)
Jordan: 26/4/7 (56%)
Celtics win. Bird wins match-up
21/04/88-
Bird: 44/10/3 (65.5%)
Jordan: 39/3/8 (51.5%)
Celtics win. Bird wins match-up.
Cumulative Stats-
Bird: 33.5/9.0/6.3 (59%)
Jordan: 39.3/4.0/7.5 (55%)
Stats are close this year but they are skewed by the one game Jordan dominated and outscored Bird 50-19. Bird still outplayed MJ in 3/4 games and Boston went 3-1.
88-89 Season:
11/09/88-
Bird: 18/10/6 (36.8%)
Jordan: 52/3/2 (54.5%)
Bulls win. Jordan takes this one easily. Bird plays just 6 games all year due to back injury and is never really the same afterwards.
89-90 Season:
11/04/89-
Bird: 27/9/6 (50.0%)
Jordan: 24/5/6 (55.6%)
Celtics win.
03/04/90-
Bird: 38/11/9 (50.0%)
Jordan: 36/6/11 (47.8%)
Bulls win.
04/17/90-
Bird: 23/5/8 (39.1%)
Jordan: 35/11/6 (54.2%)
Bulls win.
Cumulative Stats-
Bird: 29.3/8.3/7.7 (46.8%)
Jordan: 31.7/7.3/7.7 (52.3%)
Impressive showings by a declining Bird. He plays Jordan to a virtual draw.
90-91 Season:
11/06/90-
Bird: 24/11/1 (68.8%)
Jordan: 33/8/12 (50.0%)
Celtics win.
11/09/90-
Bird: 23/8/5 (40.0%)
Jordan: 41/5/6 (68.0%)
Bulls win.
02/26/91-
Bird: 12/7/5 (42.9%)
Jordan: 39/8/4 (58.6%)
Celtics win.
03/31/91-
Bird: 34/15/8 (41.7%)
Jordan: 37/7/9 (33.3%)
Bulls win.
Cumulative Stats-
Bird: 23.3/10.3/4.8 (46.5%)
Jordan: 37.5/7.0/7.8 (50.8%)
91-92 Season:
11/06/91-
Bird: 30/2/9 (59.1%)
Jordan: 44/3/6 (61.5%)
Bulls win.
12/25/91-
Bird: 8/8/4 (40.0%)
Jordan: 14/8/5 (42.9%)
Bulls win.
03/11/92-
Bird: 10/4/6 (26.7%)
Jordan: 32/13/3 (60.9%)
Bulls win.
Cumulative Stats-
Bird: 16.0/4.7/6.3 (44.7%)
Jordan: 30.0/8.0/4.7 (57.1%)
So, with both stars in their prime (from '86-'88), Bird outplayed Jordan in a large portion of the games. More importantly, Celtics went 14-3 against Chicago in the regular season and a stunning 6-0 in the postseason.
What makes Bird outplaying MJ in so many games even more impressive is that his USG% was almost half of MJ's... Bird played within his team (which was more talented though no doubt) and Jordan tried to do everything on his own which inflated his stats.