On my last trip from JFK to Westchester, I tested a theory. Are rides cheaper from the Lefferts Blvd Airtrain to my house vs the terminal? I found that the cost from the terminal was about $25 higher than from the Lefferts Airtrain station.
Fun fact: depending on which terminal you arrive at, and depending on how JFK Airtrain savy you are, the trip won't take longer than 10 minutes to Lefferts Blvd.
dh