But then again e But there again

O livro "English Guides 9: Linking Words", da Collins Cobuild, traz as duas variantes, mas eu gostaria de saber qual delas é britânica e americana.

O livro diz:

"You can use then again or there again to signal that you are about to add some new idea or fact that is rather different from what you or someone else has been saying, so you can use them to introduce an opposing argument. Both expressions are used in writing, but are particularly heard in speech. The meaning is roughly the same as 'on the other hand'."