OK see if I can write this without power going out in house again.Was much longer and more in depth, but scratch that.
Squares vs. Hex in relation to calculations and AI, VERY much doubt has any significant impact on gameplay.
Squares force more units to be affected by AOE events.
Hexes force advancement or retreat on every move, this can have a large influence on gameplay. Two units on opposing sides just want to move up one space, this movement may force them to get 2 spaces closer to each other (1 per side, draw it if you have to
).
Squares allow for much easier placement of square structures, which most structures are. Formations are easier and I imagine... easier for an art team to design battlefields.
Hexes better calculate movement in 6 directions, however VERY poorly in 2 (up and down)
Squares allow for more flanking opportunities.
Squares are easier to relate to.
Any other shapes...
Triangle... a square represents two isosceles right triangles and a hexagon is 6 equilateral triangles....so we really are using triangles.
Octagon... is what square grids usually REALLY are in a game, just the holes are filled in visually. And every unit in the game has the ability to warp past the holes.