I was there for the 92 team as well, I was 10 years old so it was one of my first Duke tournament run memories. Really, 1990 was my first time going through the tournament as a Duke fan. The 1992 Duke team is one of the best ever, but I believe 1999 was more talented and when 1999 was clicking they had a higher ceiling.
The 1999 team went undefeated in the ACC, and destroyed basically everyone, largest margin of victory ever by any school in ACC play. They ran through the NCAA tournament with the only close game being MSU in the final four (6 point W) but they were up 10-20 the whole game. Then obviously UCONN happened. Duke was the largest favorite ever in the title game, UCONN might have passed that recently.
The 1992 team lost at UNC and at Wake in the ACC. Then they also had the Kentucky Elite 8 game where we survived. However they got the job done in the title game.
I think the 1992 team was mentally tougher, and played with more of an edge, which makes sense given the personnel they had. But the 1999 team was more of a loaded roster, with more future NBA players on it, and was a much more athletic team. I believe that the 1999 teams A+ game would beat the 1992 teams A+ game. The 1992 team would find a way to will a victory out though when they weren't playing well.
To keep it brief: It's close and debatable. But the choice probably depends on which one you grew up with and were more "invested in" and for me that was 1999.