All of my grandchildren live nearer to the "other" grandparents than we do, and therefore see a great deal more of them. I found that quite difficult to begin with, since I thought that they would be the "real" grandparents, whilst we would be just the ones that had duty visits from time to time. I really felt quite jealous, and had to keep reminding myself never to let it show.
However, the situation did not quite work out like that. My first grandson decided that he really loved me, and he has never changed that position. Even seeing me about once a month, his arms were outstretched for me as soon as he set eyes on me. When the "other" and I are both there now, grandson 1 spends most of his time with me. I think I am better at playing with him than she is.
My granddaughter, on the other hand, decided that she didn't like anyone except her mummy to begin with. She would allow no-one else to hold her, not even her father! As she grew older, however, she and I developed what my daughter calls a bond, and although we don't see each other as often, she seems to regard time spent with me as more of a treat than time spent with the other grandmother.
My second grandson decided, and seems to have stuck to it, that only his own mummy and daddy count at all, although he is capable of some lovely affectionate gestures. I can get close to him when we are together, but I always need to start from the beginning again when we visit. I get the impression that the "other" grandparents experience similar treatment.
My third and last grandson - he loves everybody, but especially his granddads. And he loves my husband best of all. So he is nice to me, but soon demands "granddad, now!". It's lovely!
Moral - it all depends on the individual child, and distance is not the point.