Differences in movies shot with digital cameras

[diamondfoxxx]

I was hoping someone could clarify why movies shot on high definition digital cameras look different: to the casual viewer, when watching 'Apocalypto' (as an example) on a high definition format like blu-ray it will look absolutely gorgeous. But show another movie shot with high definition digital camera--let's say 'Miami Vice'--it looks like a movie shot incompetently with all the grain around. I understand that these two movies were shot on different cameras AND that artificial grain was added in 'Miami Vice'.
What I want to know is this:
1.) If Mann decided to NOT add artificial grain to Vice would it have looked like Apocalypto?
2.) When shooting digital during low light scenes, does video noise always pop up?