There are many good day schools in the United States that are comparable to the top 100 boarding schools. One of the benefits of boarding schools is that the student is able to spend evenings with their friends, such as birthday parties, events in the dorms, etc. This way they have a venue to practice their English every night so they can improve more quickly.
For home-stay students, it really depends on how much the host is willing to talk to the student. The best way for students to learn English is by communicating with their peers who are native speakers. Since they are able to talk about things that adults may not talk about, they have more chances to express themselves. Also for boarders, since there are advisers in the dorm, the students can also talk to them if they need to practice with adults.