I have often wondered if what I saw the Xbox 360 put out would have been possible on the Xbox. My conclusion is: no, it wouldn't have been. It would have been a scaled-down, lesser experience. The consoles are power-beasts this generation and can barf up some very impressive things. Not only in terms of graphics do the games provide a better feeling, but also in amount of enemies on-screen, AI and animation. The latter plays a big role in gameplay.
I also like in-game cut-scenes. The Xbox could do that, sure, but for the first time they actually look like something worth watching. No blocky polygons and blurry textures to distract you from the story that is unfolding. I appreciate all the people shouting "Gameplay over graphics, rawr!!" but they are both important. The fanatics can play with their emulators, if they'd like, but I do like a good graphical experience (both on consoles and PC).