Yup, you are pretty much reading my mind here.

I still remember Rose's wide eyed look at the idea of a Christmas that had already happened once, and it's gone, and the way she stepped on the snow.

To elaborate, I also felt like she immediately tried to relate to the Doctor as a person, noticing that it's probably "better with two". That moment where she looks at him and essentially realizes he might be lonely, is a lot more powerful than the moment where Amy is stating all the things that are problematic with the Doctor's life while looking at the screen. The way that the eyes of the Nine and Rose met there was a sense of connection. Here they are hardly looking at each other, it's like they are not interested in each other enough to look. The best part about the companions for me has been their ability to make the Doctor "watch" them, and he was always focused on Rose, Martha and Donna. And they were always focused on him, aware of where he was at all times. I just don't get that sense of a connection between Eleven and Amy. And so I find it difficult to relate.