Virago said:
Even on an open field, the squares with 5/10/5 are not significantly less accurate than hexes
You are correct for straight line movement. Hexes and squares (using 5/10/5) are virtually identical in those circumstances, regardless of distance or direction.
However, for non-straight line movement, squares start losing a little accuracy.
For example, with hexes, if you are 10 feet away from an opponent and you want to get to the exact opposite side of him while staying 10 feet away, you will move 30 feet to get there.
With squares, you will move 35 feet.
The reason for this is that you are moving in a more circular path with hexes. In fact, the circumference of a half circle with a radius of 10 feet is 1/2 * 2 pi * 10 which is 31.4 feet. Closer to 30 than 35.
So, a lightly armored and encumbered medium sized character could do this and still get in an action with hexes. With squares, he could not.
So, it could make a difference. And just like the AoO example, the grid system should not affect the results, but it does moreso with squares.
Virago said:
-- and they are more accurate for big area type effects, where 5/10/5 and squares gives you something vaguely circular, and hexes just give you a big hex.
Huh?
A hex is nearly circular. So, even a large hex is just as accurate with respect to a circle than a bunch of squares. And, it is much easier to figure out which spaces are included and which are not. For example, look at the Sleep spell diagram on page 69 of the DMG. It looks more like a cross than a circle. But, a hex pattern of 7 hexes across (you ignore the center hex for spread, bursts, and cylinders) looks almost exactly like a circle. Granted, it is still a large hex. But, unless you get to extremely large sizes, you would not include any additional edge hexes even if you drew a large circle on the mat with a compass.
Since most area effect spells in DND are less than 30 feet in radius, hexes are not only just as accurate, they are also much quicker to figure out.