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Delta's terminal at JFK is positively claustrophobic; its entrance area traps exhaust fumes, has bad lighting at night, and is just poorly designed.
AA at JFK is unfriendly inside the terminal. The worst part of it is the distance you have to walk to get to the gate (first going down the escalator, walking a long distance, then going up another escalator); it's airport terminal design at its worst. I also found the security guards at JFK's AA terminal sadistic. (If you're in a hurry just because you're missing your flight, it's more likely they'll stop you.) They don't seem to be so much diligent as intent on ruining you travel experience. This is one terminal to avoid.