I decided to check out how each championship team ranked in some categories to see if there was any correlation between a particular aspect of the game and winning. I chose Points, Rebounds, Assists, Personal Fouls Committed per game, Personal Fouls Drawn per game, and opponent points per game. I chose these particular categories because they encompass many important aspects of the game. Of course much of the game and what teams do lies outside of these categories but if nothing else we can take away some trends. All of these are pace adjusted. The following study shows championship teams and what place they finished in during the regular season:

Championship teams averages per 100 possessions:

1998 Bulls:
9th in ppg, 1st in rpg
5th in APG, 25th in Personal Fouls per game.
18th personal fouls drawn per game, 3rd in opponents points per game.

1999 Spurs
11th in ppg, 3rd in rpg,
5th in APG, 26th in PFPG, 20th in PFDPG.

2000 Lakers
5th in ppg, 1st in RPG,
8th in APG, 20th in PFPG, 3rd in PFDPG,
1st in opp pp 100

2001 Lakers
2nd in PP 100, 4th in RPG, 8th in apg, 14th in PFPG, 4th in PF drawn per game, 21st in opp pp 100

02 Lakers
2nd in ppg, 5th in RPG, 8th in APG, 10th in PFPG, 7th in PFDPG, 6th in opp pp 100

03 Spurs
7th in ppg, 8th in RPG, 23rd in APG, 25th in PFPG, 3rd in PFDPG, 3rd in opp pp 100

04 Pistons
18th in ppg, 3rd in RPG, 13th in APG, 21st in PFPG,
3rd in PFDPG, 2nd in opp pp 100

05 Spurs
9th in ppg, 3rd in RPG, 9th in APG, 26th in PFPG, 8th in PFDPG, 1st in opp pp 100

06 Heat
7th in ppg, 3rd in RPG, 14th in APG, 18th in PFPG, 8th in PFDPG, 10th in opp pp 100

07 Spurs
5th in ppg, 10th in RPG, 5th in APG, 29th in PFPG, 19th in PFDPG, 2nd in opp pp 100

At this point I think the reader knows which categories are which, so I'll just list the place finishes. It goes ppg- rpg- apg- pfpg- pfdpg-opp pp 100:

08 Celtics
9th 8th 7th 3rd 3rd 1st

09 Lakers
3rd 7th 3rd 22nd 11th 6th

10 Lakers
11th 1st 16th 29th 13th 4th

11 Mavs
8th 9th 1st 26th 20th 8th

12 Heat
8th 20th 21st 16th 7th 4th

13 Heat
2nd 29th 6th 22nd 9th 9th

14 Spurs
7th 15th 1st 26th 27th 3rd

15 warriors
2nd 16th 1st 22nd 29th 1st

16 Cavs
3rd 4th 10th 11th 8th 10th

17 Warriors
1st 18th 1st 23rd 26th 2nd

Average place finishes of championship teams from 1998-2017:

Points: 6.5th place
Rebounds: 8.4
Assists: 8.3
Fouls: 20.7
Fouls Drawn: 12.3
Opponent points: 4.9

Interestingly enough, the evidence I found suggests that the style change of the NBA we see today took it's biggest step in the 2012 season. Here's what these same numbers look like between the 1998-2011 seasons:

7.6 4.7 8.2 20.6 10 4.9.

Conclusion:

To me it seems that defense is the most important aspect of the game. This would reinforce the old saying of "defense wins Championships". The next important aspect of the game is rebounding. This makes sense, as rebounding gives you possessions, and the more possessions you have the more you can score in the first place.