Well, they key thing isn't the FTA, it's the underlying charge that you need to look at. An FTA is a pretty minor thing and most likely won't result in extradition -- but what the person didn't show up for in the first place is a different matter.
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.