Squares have a contiguity problem: does a square in a grid have 4 neighbors (rook contiguity) or 8 (queen contiguity)? Hexagons do not have this problem. All neighbors of a hexagon share a full edge, not just a vertex. All neighbors of a hex also have their centers equidistant from that hex. A massive number of spatial problems turn on neighborhood definitions, and hexes are almost always a better representation of reality than squares.
But if you assume rook contiguity then it seems equivalent to hexagons. All neighbors share a full edge, all neighboring centers are equidistant.
I get that you're saying hexes are almost always a better representation. I still don't see a concrete example of why, for geographical indexing specifically.
[Edit: sibling reply explained that at the end of the day, it's not about indexing but rather route planning.]
Let's say you are looking for the closest gas station. One that is in the close corner of a "diagonal neighbour" would be closer than most points in the "edge neighbours". So if you want to find something nearby, you'd usually want to look at all 8 neighbours. The hexagonal neighbours look more like a circle centered in the original hexagon, thus more convenient for that purpose.
