It doesn't change particularly much from what the video showed you, to be honest.
A classic (purely 2D, think Sega Sonic) and modern version (blend between 2D and 3D sections, though arguably more 2D compared to the other more recent Sonics) each of 9 stages/worlds with boss battles after the third, sixth and ninth stages. Generations is easier than Unleashed and Colours until the final stretch (Stages 7-9 is where it picks up a bit with precision platforming), causing less disruption to the flow of the game due to requiring less trial and error gameplay.
There's also 5 red rings for each classic and modern stage that you can grab to unlock some goodies for the art gallery and music room in the game. Finally, there's also 5 challenges per classic and modern stage, ranging from simple time trials to gimmicky stuff such as the stages being made into obstacle courses and requiring you to get through them unscathed. I'd say it's a very well done game that is more or less a love letter to all the generations of Sonic games; regardless of their reputation.