Hexes look sci-fi, squares look dorky.

In your opinion, perhaps.

Hexes provide better distance approximation for fixed-increment movement.

I still don't see why this matters when the tiles in GCII and GCIII clearly don't represent uniform amounts of space.

Both suffer from the "wiggle" problem when moving distances. Both have the same solution to that problem, which is simply a smooth pathing issue inside the game engine.

Hexes also have six directions of movement along which they will not 'wiggle,' whereas square grids have eight.

One thing;

Moving diagonally on a square grid as opposed to a hexagonal one gives the unit in question more effective movement than one who travels in the direction of the faces of the square. This is an "exploit" of the game's hardcoded limitations, and it gives the player who abuses this quite an advantage. Everything else is just gravy really.

As I have said several times so far, including in the post to which you responded and once before in this post, I see no reason why the absolute distance traveled on the grid should matter when the grid tiles clearly do not represent uniform amounts of space. Beyond that, it is also possible to map a circle into a square grid in such a way that moving along the diagonal of the square grid represents moving along a diameter of the circle, which would make the distance distorted by the grid rather than different.

Moreover, when mapping three dimensional surfaces to two dimensional planes, hexagons are at best no better than squares, as far as distorting distances goes, and may even be worse when mapping spheres (and hey, guess what shape planets resemble?) because there is a way to map a rectangular grid onto a sphere which has no non-quadrilateral components in any but the polar regions, while there isn't such a layout for a hexagonal grid. If you're looking at a region of a curved surface which is small enough that it can reasonably be assumed to be flat, then sure, a coarse hexagonal grid works better than a coarse rectangular grid if you're trying to avoid distorting the distances covered by a move action. If you're trying to fit a sphere's surface to a planar grid? Not so much. By the time you're mapping essentially arbitrary points in 3D space to a 2D grid, as is done in the GCII and GCIII game map, the grid already represents something where the distances are so badly distorted that I really must wonder why anyone cares that the length of the diagonal of the square isn't the same as the length of its edge.

Also, the distance isn't that distorted - after all, the distance is in units of tiles, not any absolute distance unit. The tile in the center of a 5X5 square of tiles is two moves away from any tile on the perimeter of the 5X5 square, and 1 move away from the tiles on the perimeter of the 3X3 concentric square, and 3 moves away from any tile on the perimeter of the 7X7 concentric square. Since there's no obvious relationship between the shape of the grid, be it hexagonal or rectangular, and the space represented on the map, why does it matter that the absolute distance between one corner of a square and the diagonally opposed corner is ~40% greater than the absolute distance between the corner and any corner on the same edge while the error in absolute distance is less with a hexagonal grid? The absolute distance on the map has no clear relationship to the absolute distance in the space represented, anyways, regardless of which type of grid you're using, and since it's the move actions which are related to the travel time and moving from any tile to any adjacent tile always costs only one move it doesn't matter for that, either.