Is the battery life of a refurbished MacBook Air with a new battery the same as a new one?

Yes, essentially the same — a new battery has the same cycle count and capacity as one in a brand-new MacBook Air. The real difference is in other components like the SSD, keyboard, and trackpad, which have some mileage. For pure battery life in everyday use, you won’t tell them apart, especially if Apple or a reputable shop did the replacement. Apple refurbished units come with the same warranty as new, so that’s the safest bet.