Why choose an adult Boston Terrier? For someone considering breeding, a young adult may give greater certainty as to quality. Also, some people prefer an adult dog since they are probably already housetrained.
Adult Bostons are usually adaptable to the "house rules" and are rarely chewers. However, an adult dog will have developed behavior patterns. These may or may not fit into your routine. If the adult Boston you select has not been housetrained or hasn't been exposed to children, some additional work will be required for everyone to adjust.
Usually, adult Bostons adapt just fine to a new owner, their environment, and their lifestyle. You may want to consider taking an adult BT on a trial basis to make sure the relationship will work.
Sources for adult BTs include: rescues, shelters, and breeders who will no longer be breeding the dog. Sometimes, breeders will get a dog back because the owner moves or cannot keep the dog for some reason. With so many BTs in rescues and shelters, and being able to skip the hassle of common puppy problems, an adult BT is definitely worth considering.