TBC did bring paladins to horde and shamans to alliance which already changed the dynamics a lot.
Also the end of 40man raids, obsoleted old world, arenas, flying, dailies. No more can you grind on your own pace, you have to wait for dailies to reappear.
The end of adventuring around the world, instead turned into quest hubs that lead into the neighboring hub and the game has been like that ever since.
Wouldn't call anything classic period except original itself. TBC is still a good and interesting game, but not classic. It removed and changed so much of the feeling of original one.