Which is best: a ball head or a 3-way head

Nando, Photofacts staff and readers, first of all, best wishes for the new year. I read the above article with great interest. Thanks for the tips.
A number of years ago I bought a tripod from Redged complete with a ball head. I always had the problem of it 'sagging' after setting it, which made precise adjustment simply impossible. I was advised to buy another ball head with a larger ball that could be clamped better. It became a fairly heavy ball head from Sirui. That solved the problem of the 'sagging'.
My own stability also became a problem over the years and then I thought I could solve this by also starting to use a monopod. That is less heavy than always having to carry a tripod. I bought a Carbon monopod from Sirui that has fold-out feet so it can stand independently and then put my Sirui ball head on it. The effect is that the ball head feels heavier than the monopod. Because the monopod has fold-out feet at the bottom, there is also a ball head on those feet. It is not wise to use portrait orientation by tilting the ball head. The camera then hangs 'beside' the monopod, meaning there is no stability anymore. That can also happen with a tripod. To solve that problem I bought myself an L-bracket and the camera is now always positioned exactly in the middle of the monopod or on the centre column of the tripod.

I also started out with a ball head back in the day. The problem with that is working with longer lenses. When you loosen the main screw, you always have to hold the camera properly if you want to avoid the lens crashing into the tripod. As described in the article, I prefer to use the ball head when travelling. That is why I have been working with a gimbal head for years. Once properly adjusted in balance, the camera, even with a long zoom lens, always remains balanced when loosening it. The camera can be adjusted very smoothly in horizontal and vertical directions. With a longer lens, you soon have a foot (or little foot) underneath the lens, which makes it easy to switch from landscape to portrait orientation. But when the camera (with a shorter lens) itself is mounted on the gimbal, you have to use an L-bracket to be able to switch smoothly.

Hello Nando:
The image you show is indeed a three-way head, but it is a "gear" version.
https://www.cameranu.nl/nl/p2394725/benro-gd3wh-precision-geared-3-weg-kop

"Gear" means that a worm and worm wheel are used to adjust the axis. The construction means that this axis is automatically locked.

Here is the image of an ordinary three-way head, which can also be adjusted along 3 axes.
https://www.cameranu.nl/nl/p2211605/benro-hd2a-arca-swiss-3-weg-statiefkop

In most versions it has 2 handles, one for the "tilt" movement and one for the "roll" movement. By tightening the handle, you clamp or release that axis. On the "pan" movement there is only a knob to lock and release it. This is the type of head that is often included with cheaper kits .
Tilt: from top to bottom;
Pan: from left to right;
Roll: rotating movement of the camera.
On certain three-way heads there can be a handle on each of the three axes:
https://www.kamera-express.be/manfrotto-229-3d-super-head

Do you want a geared head? For the price, you don't have to leave it
See for example: Arca Swiss D4 Classic