"thường" is more common than "thường xuyên"
not really, they have different meanings and are not interchangeable.
Which would be best here? Or would it depend?
yes it depends.
So "thường' almost equals "always?" Or "always with maybe an occasional lapse"?
I'd say "on a regular basis", not always but most of the time.
Con mèo của tôi thường xuyên ăn túi thức ăn vị cá biển cho mèo. :-)