Here's the way I see it:
--Round has a huge advantage: it's natural. It's difficult to find a straight piece of timber or bamboo with an oval cross section. You need a curving branch to get an oval. If you're building with bamboo or if you want to use a long handle, round is a very good way to go. The downside, of course, is that it can be hard to keep the blade oriented properly for a cut. One solution (used only in Indonesia, to my knowledge) is to cut a small groove down one side, so you can align with the groove. Others like to change circles into octagons, with is complicated (I've tried doing it), but possible with the right tools and/or skill.
--Elliptical or oval has a huge advantage: it fits into people's hands and helps align the blade. It is also naturally available in curved pieces of wood from branches. More often, though, it needs to be cut to shape, and that takes a bit of skill. This is a good option for handles on cutting blades or impacting heads, where alignment is critical. There aren't a lot of round axe handles out there, for example.
--Rectangular has a huge advantage: alignment and realignment. Not counting cooking and pocket knives, I have two square-hilted blades: a western fencing saber (flattened on the back for the thumb) and a replica bronze age leaf sword. The squared hilt on the bronze sword is particularly illuminating, because it is formed by an H-shaped bronze piece (in line with the blade) holding two slabs of wood on the sides. At first, this may seem backward. Wood is worse at transmitting shock than is metal, which is why you typically want the wood hilt meeting your hand, not the metal tang (this is the reason for rat-tail tangs on things like kukris, incidentally. The solid wood hilt is supposed to act as a bit of a shock absorber). However, bronze has a problem: it's softer than steel, and the blade is designed for cutting and slashing. It will get dull. The great thing about that square hilt is that you can quickly rotate it 180 degrees (the corners make it easy to spin), and the metal ribs tell your hand exactly where the edges are without you having to look. I think rectangular hilts are a great idea in double-edged blades, where you need to be able to flip from a dull edge to a sharp edge quickly. So far as I know, this was best implemented in bronze-age leaf swords. The problem, of course, is that sharp corners are lovely for raising blisters, and it's annoying how many modern knife makers have forgotten this in their quest to make flat pocket knives and such.
My 0.002 cents,
F
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