In most of New England a Failure to Appear is a felony. You will be arrested by whatever state you're in as a fujitive from justice and you will then be handed over to the state holding your FTA re-arrest warrant. After you go through court and get sentenced in your home state, you will be shipped to the arresting state to face the Fujitive from Justice charge.
Your question has already been asnwered. It depends on the original charge, and also if Failure to Appear is a felony in either state.