The two forms are interchangeable in meaning, and I am not aware of one form being more literary than the other. I think there are slight regional tendencies towards byddai in the south and basai in the north, but ultimately it’s simply speaker’s preference – feel free to use whichever you’re comfortable with.
Well, using Google Translate is certainly a double-edged sword, and usually you need to have a certain grasp of a language in order to gauge how good (or usable) a translation really is. And of course, usually there is more than one way to express something, and if Google for whatever reason chooses a specific structure over another, that doesn’t mean that one is “more correct” than any other.
For example, the question “Do you have a car?” comes back as “A oes gennych gar?”, which technically is a correct translation, but sounds like it comes from a time at which said car was likely pulled by horses.