Having said that, the difference I have found is that the Eastern method uses more leaves in a smaller pot but a shorter steep time and then has multiple steepings. Here are the ways I brew:
For the Gongfu method, I put a teaspoon of leaves per cup of water that the pot will hold and then steep from 1 to 3 minutes- pouring off the entire pot as soon as it’s steeped and refilling with more hot water anywhere from 3 to 7 times depending on the tea. (I also feed the teapot and the teapet but unless it’s a Yixing pot, that’s not necessary.) For the Yixing pot, I heat the pot first with hot water poured off immediately and then ‘wash the leaves’ by filling the pot and pouring it off immediately. (I save this wash water to wash the pot with when I’m finished.) Then I’m ready to fill it again and make tea.
For the Western method, I choose a different teapot and use a teaspoon of tea per cup. I only warm it if it’s a particularly delicate pot and I don’t wash the leaves. I use water from 195° (for white teas) to 212° (for oolongs and black teas) and steep 2-5 minutes- usually 3. When it’s ready, I pour into a cup and enjoy. I do usually use small pots so I get a mug or a mug and a half of tea from a pot.
I would say use the method that makes the tea you like best and don’t worry about how anyone else does it. Most of the time teas will give you times and temperatures for optimal brewing on the package and you can use that as a starting place.