I always got the sense that Anastasia and Maria were not as close with Tatiana as the were with each other or Olga. I think it's clear that O & T shared a special bond and that Olga's affection for Maria may well have exceeded even that. Anastasia and Maria were clearly very close as well. I can see T perhaps caring slightly more for A on account of the age difference and that true big sister-little sister maternal vibe. But of course this is all rather speculative.
What seems obvious is that they were all very close and forced to, in many ways, create a tight-knit unit. Most groupings such as OTMA(A) will feature some type of sibling rivalry, but that seems almost non-existent here. Olga submitted to Tatiana in a surprising way that one might ordinarily expect to see from a sibling several years younger (not 19 months older). Maria meanwhile, despite her age and size advantage, seem to express no qualms about Anastasia calling the shots. Then of course once you throw Alexei into the mix you have a rather unique situation.