If you want diced onions, the cook generally wants onion chunks below a certain cubic mass, so they cook and dissolve easily and uniformly. It does not matter if some pieces are 50% of that size, some are 20% and some are 80%.
With that, 1-2 horizontal slices and a bunch of straight downward slices are the safest and easiest way to achieve that.
That technique also expands to onion rings, sauteed onions and such.
Just the opposite! When sautéing, too-small pieces have burned by the time the larger ones have cooked, giving the dish a bitter burnt flavor and ugly black flecks.
Burnt bits add unpleasant acridness to the finished dish. And pieces that are 20% of the general size are very like to be overcooked when the rest are properly cooked, so limiting those is important.
When cutting potatoes into chunks, for something like a stew, I often find myself thinking about this problem, and how I would write a program for a robot to do it.
They are fairly well approximated as ellipsoids of different sizes. Typically, I want pieces around half the volume of the smallest potatoes, but with the range of sizes, this means cutting the larger ones into at least 5 pieces.
While it would be simple to make parallel slices giving equal volume, these would have very different shape to the halved smalls. Some can be quartered to give nice chunks, others into thirds with 2 perpendicular cuts...
If you want diced onions, the cook generally wants onion chunks below a certain cubic mass, so they cook and dissolve easily and uniformly. It does not matter if some pieces are 50% of that size, some are 20% and some are 80%.
With that, 1-2 horizontal slices and a bunch of straight downward slices are the safest and easiest way to achieve that.
That technique also expands to onion rings, sauteed onions and such.