Yes, the gym leaders/elite four have the same teams as before, the first time round you battle them. (Although levels may have changed for a few, the movesets are definitely different/better, and with Red he got a significant level boost and slight changes to his team i.e. Lapras for Espeon).
Also, once you beat the game you can refight the gym leaders and elite four, and the 2nd time onwards you fight them they get far higher levels and a new team, including 3rd and 4th generation Pokemon.
Try the Questions and Answers thread next time, please. Answered, so closing.