The problem with NYC hospital based 911 EMS is that can be prohibitively difficult to get in. There are legions of EMT's in NY. The vast majority of them have the goal of doing NYC 911 EMS. Many apply to FDNY right away, then look for work in the meantime. It's common to start in private IFT, typically Transcare, since they also do 911. The hospitals pay much better than FDNY, and the pay progression can be quicker. On top of the competition from other applicants, most hospitals want prior NYC 911 experience to get in. Add to that all the recently unemployed experienced EMT's from the multiple hospital closings in the SVCMC system.
A good number of FDNY EMS leave there for the hospitals as they pay better, have better schedules, less mandations, and overall better working conditions. If you just want experience, but don't plan to stay at FDNY EMS for the long haul, then a hospital would be a home run for you. Otherwise, FDNY is definitely more desireable than the privates. As far as pay, the privates pay around 10/hr. For a 40 hour workweek, a rough estimate of yearly salary is 2k/yr for every $1/hr, as a slightly lowball estimate. That's around 20k/yr. The real number is actually $20800/yr. FDNY starts at 27,295. That's almost a 7 grand a year difference, less your pension contribution, of course.
http://www.nyc.gov/html/fdny//html/community/ems_employment.shtml#emt_salary
Consider also that the privates generally don't give much in the way of raises, whereas FDNY EMS tops out EMT's at 39,179 after 5 years, which is around 20/hr, the same as a medic in the privates.
Do the math with tolls, and consider that FDNY may send you to the Bronx, Staten Island or whatever, and at different times of the day, so you may be fighting traffic both ways. Plenty of OT though, voluntary or through mandation. Fun job, great for experience, but you'll probably burn out with the FDNY drama and BS after a while. I used to work hospital based EMS, primarily 46E and 46Y, along with 53D, 53G, 53J, 53I, 54G, 53Y and 54Y to a lesser extent. I recommend tour 1's, as you see all the night creatures and all sorts of deviant behavior.