Yeah, that Jags team was incredible, but also the team might have been better and drawn Tennessee in the opening game. They win, the Bills beat Seattle, and the Dolphins go to Indy instead of Jacksonville. Marino plays OK, the defense holds together, and the Dolphins get the upset, heading to Jacksonville where they...lose a mostly defensive battle, something like 21-10.
The wrinkle? Marino comes back in 2000. That season had the potential to be magic. Imagine if Marino goes out on top in 2000 and the Dolphins draft Brees in 2001 - holy shit do we have an awesome team. By now, the Pats and Dolphins would probably share about 6-7 more titles rather than the Pats dominating, and expect to hear the name Drew Bleeping Brees a lot.
I don't know if the Pats would be that great in this world. It depends on how Dom Capers does as their HC (Kraft was ready to hire him before he was able to agree with the Jets on compensation for Belichick). They may have Brady (outgoing personnel man Bobby Grier drafted him), but he's a product of the Belichick-Ernie Adams cheating system to a fair degree, and he may not get as much of a chance with Capers as coach.
Side note: Allegedly, the Pats also wanted to interview Rams OC Mike Martz that off-season as well. However, the Rams said that he would be the guaranteed successor to Vermeil for the HC job if he didn't take the interview. He agreed. Vermeil got upset at the Rams for doing that, he resigned, and Martz took over.