NY is a good place to BE from, but not to spend your life or career. If you want to do FDNY EMS, you'll probably have a good chance of being hired. Use them for a few years(or 5 to be vested), and use them for a resume booster. It's an awesome job for a few years or so, but you'll eventually be fed up with the bs. If you have any serious considerations about trying out FDNY EMS, give me a PM and I'll tell you what I know.
FDNY EMS used to be NYC EMS under NYC HHC. Working conditions were a lot better prior to be absorbed by FDNY. It drove many to hospital based 911 providers. A FDNY medic is set to graduate from the Fairfax FRD at the end of this month. Attrition is high there.
Your learning curve will be steep in NYC, you'll be like a machine in no time. Do it, and take your skills somewhere with a better retirement and working conditions. That's what I did. IT's ALL ABOUT THE BEST RETIREMENT! I can't stress that enough. When I'm 60 I'll use the DROP money to pay off my second and/or third house, and live comfortably on my pension, which I can count on until I die.