GH2 is a bit more forgiving about precision, but the biggest difference is in the HO/PO (hammer ons and pull offs). These are sequence of notes where you just need to strum the first note, the others just require you to press the buttons at the right time (notes without the black circle around the white dot).
In the original GH, on these sequences you have to hold all the notes togheter and release them as you play a pull off, or in the case of a hammer on you play the first note then all the others without releasing the notes already played. I can't describe it better than that, sorry.
Anyway, on GH2, in a hammer on or pull off you don't need to do that, you can play the first note, release the button, play the second note, release the button, etc. Much easier.