Team latin, especically when talking to gardeners. If setting up a plant trade or seed trade, it's the only way to make sure each party is on the same page. I don't want someone using a common name which might be the common name for 10 different plants.
I use common names when talking to non-gardeners. Most of my friends are non-gardeners. They refer to plants in terms like "that big purple thing growing beside my house".
Karen