Sautéing in oil allows you to really crank the heat, using butter you have to be more careful. Cutting in larger chunks is great for some dishes and bad for others. The whole timing thing is probably the hardest to nail, going easy on the heat allows you to get in some other prepwork while the onions are doing their thing, but you also don't want to spend hours cooking so you want to crank it to the point where your prep and the onions will be done at the same time.
How far do you take the onions? How far do you take them if you want to throw in more veggies into the same pan? When do you add spices if you want them to get a bit toasty aswell? And sautéing large amounts of onion (1kg+) is a whole different calculus.
Cooking is this endless fractal of problems to solve and optimize. Kinda like programming innit.