Maybe my children just have a different personality
There are differences in personality and so different approaches may be needed. I have 3 and each one of them requires a slightly different approach. We very rarely hit or yell at our kids (usually it's when the put themselves or the others in danger - e.g. running out into a busy parking lot) - I wont lie and say it never happens. However, one of them likes to follow (i.e., you create a precedent with her sixter and she happily adheres) another one needs to be appreciated so motivation about how it will make everyone happy is helpful, the third likes to stick to schedules so telling her she'll be late or that she'll earn a star for being on time motivates her to be ready and get her siblings ready too. Stickers, mini-treats and the like are very useful as well when appropriate.
I think it's silly to say "there is one best way" - discipline methods are a tool, and you should have several tools in your belt, and use the most effective tool as often as you can. I'm glad to learn about more effective approaches that don't require shouting and/or hitting.