British English is the most rigorous in grammar, wording and sentence making, and its pronunciation is also cadence, which reflects its rigorous side. When it comes to Britain, the first thing that comes to mind is its long history, and the other is a word "gentlemanly demeanor" that originated in Britain. So British English is more suitable for formal occasions.

American English has looser grammar and smoother pronunciation. The most striking feature is the extensive use of "slang" (you can take the well-known Friends as an example). Compared with British English, American English uses more phrases and more extended words, so it is more natural and warm to use American English in life.

I hope it helps you.