There's no realistic way to say who would win in a one-off match, but if we're comparing overall seasons then the 08 team was better. The 99 side were far more exhilarating and remain dearest to my heart, but that whole season is like a fairy tale given how many times we were behind in massive games only to snatch victory from the jaws of defeat.
Think about each competition; in the Champions League quarter final we were an overhead kick off the line away from going 2-0 down against Inter, before Scholes came to the rescue in the 88th minute. Then we needed a 91st minute Giggs equaliser to rescue a 1-1 home draw against Juventus in the first leg of the semis, and an even more improbable comeback from 2-0 down to secure a 3-2 win in Turin. And then to top off these absurdities, we go one step further and score two injury time goals to stun Bayern in the final.
In the FA Cup, two injury time goals were required to advance against Liverpool in the 4th round, then there was the classic semi against Arsenal where in extra-time we survived a Roy Keane sending off and a Dennis Bergkamp penalty miss before a ridiculous winner from Giggs saw us through to the final.
Then we get to Premier League, where we were only one point ahead of Arsenal going into the final day and went 1-0 down to Tottenham, needing a Cole equaliser and Beckham stunner to seal the trophy.
In contrast, the 08 team, though not nearly as exciting, were absolutely ruthless and efficient, frequently putting games to bed in the first half before strolling to victory. Also, with the possible exception of the CL Final that went to penalties, we always looked like the strongest team in both the PL and CL. We were far more tactically aware than in 99, hence our magnificent CL run for several seasons after this, where miracle comebacks were no longer required to get results.
So yeah, 08 > 99 in terms of pure performance, even though 99 is the single most exciting and guttiest season produced by any football club in my opinion.
* If the 1999 team were as well drilled tactically as the 2008 team then I'd likely back the former, but we'll never know how they would have performed using a similar setup.