From what I can tell people like her because she's young
feisty and has long legs
Donna took no nonsense from the Doctor and went from being a superficial trite self absorbed irritation to a warm compassionate human being with a deep love and understanding of 10. There was true respect/friendship between them and both benefited from the experience. I see no evidence of this with Amy.
I can understand the Doctor being drawn to Amelia but aside from curiousity as to what surrounded Amy I am at a loss as to why he would continue to have her travel with him. Especially after she got her family back and married Rory. He's left companions behind for less
That aside I always assumed Amy's two dimensional character was deliberate - as a result of the crack in time -
with the airing of the christmas specials/mini episodes I've had to put that theory to rest