Air train works best (and is a terrific option) if you only have carry on luggage or a big wheelie bag. Navigating Air train with several bags can be difficult.
Physically, Newark is closer than JFK. JFK is a world class airport, but not nearly on par with airports like Hong Kong, but certainly better than LHR. Ever since I was a kid growing up about 20 minutes from JFK, that airport has been under construction in one way or another, and it's never ever stopped. Your experience at JFK will largely depend on which terminal you arrive at. It was designed in the 50's and 60's and consists of separate terminals, where each terminal services one or a few airlines, except for the International Arrivals terminal, which services most smaller airlines arriving and departing from JFK. AA, UA, BA, DL, etc all have their own or shared terminals with their own international arrivals and departures. I don't remember which terminal BMI uses, but you can check the Port Authority of NY and NJ web site. The Port Authority runs all 3 NYC area airports (LGA, JFK and EWR) and they also operate bridges and tunnels connecting NYC and NJ.
The JFK Air Train has an inner loop train (free) connecting all the terminals. The outer loop connects all the terminals with the rental car center, Howard Beach subway station and Jamaica with the connection to the LIRR train to Penn Station which is located at 33rd Street between 7th and 8th Ave. The connection is pretty good, with elevators to move you from the upper level where the Air Train is to the LIRR train platforms. There are elevators at Penn Station to get you from the train platform levels to the concourse level, and escalators that lead up to street level. The Air Train to Jamaica is $5, and then the LIRR ticket to Penn Station is about another $7 - $10 depending on when you are going. (LIRR has rush-hour pricing for rush hour direction, to the city in the morning rush hours, from the city in the afternoon/evening hours.) There are ticket machines to buy both your Air Train and LIRR tickets when you arrive at Jamaica. (just before the exit, on the right when you enter the exit hall.) Jamaica Station is the LIRR hub, so trains leave from there to Penn Station very frequently, and depending on which train you take it's either 0, 1 or 3 stops to Penn Station, and that part of the trip takes about 25 minutes.
Newark is (well, for lack of a better word) Newark. (Sorry in advance to you Newark fans.) It's a lot smaller than JFK and closer to the city. I assume you mean Manhattan when you say New York City. From Newark you take the Air Train to the Newark Airport train stop, and pay $5. From there you take the train to Penn Station. I have no idea what the cost is for the NJ train or how frequently they run.
If you're making your decision based on airfare cost, then it doesn't matter. Either one works. If you're making your decision based on convenience, I think it's a toss-up. I'm not sure if Newark's runways can handle 747s or not. Somebody that frequents Newark will know.
-David