Not all out of State warrants are going to result in extradition. Prosecuting agencies in Florida will extradite on more serious crimes but generally not on failures to appear for misdemeanors. If this individual is likely to be in jail in New York for a long time, he may actually benefit from having the Florida warrant served on him. Once the warrant is served, if he is still in jail he will begin accruing credit time served for his jail days.
He should consult with an experienced criminal defense lawyer who can properly advise him on how to get the best result for both his NY and Florida cases. Good luck.
It really depends on whether the state of Florida still wants to prosecute the person. The state will have to file a detainer which will indicate to NYS or NYC corrections that Florida intends to extradite. That way, once the sentence is up in NY, NYS or NYC corrections will hold the person and give Florida a reasonable time to come pick him up. It depends on the offense. Sometimes the state will not bother to extradite when the offense is minor.