It has to be mentioned that garlic will taste different depending on how it is cut, or not cut. Minced v sliced v whole, and raw v lightly sautéed v roasted. Minced garlic generally shouldn't be sautéed more that a few seconds until aromatic, or they just taste bitter and burnt. Unless of course that is what you are after.
Onions also provide texture and body as well as flavor. Sliced v chopped v brunoise v minced also have flavor differences when cooked simply as a result of size. I think everybody here know this, though.
But method depends entirely on the dish. Sometimes sweating onions to translucent is desired, and other times caramelized for depth of flavor. Sometimes crispy onions or shallots add that flavor as a garnish on stews, where the base onion is simply sweat until translucent at the beginning. I've made other dishes where the onions are sweat for a long time, but not caramelized. How they are cut, as I said, depends a lot on what the desired effect is. I can't remember the last time I cooked spring onions for any length of time, other than grilling. I usually toss them sliced into curries or soups in Thai or Chinese (inspired) dishes. And potato salad. : )
I do have a pet peave : I can't stand it when caramelized onions is listed as an ingredient in food and what you get are just chopped and sweat until just past translucent. Caramelized onions must have color. Lots of it. Thickness of slice is also important. I personally prefer thinly sliced, but I've seen fat slices and roughly chopped, as well.