Really impossible to answer without more specifics.

For starters you need to secure your award ticket before choosing -- are both ORD and JFK currently available? What airlines are you proposing to fly? Are they partners (in which case there might not be a need to collect at the domestic terminal and then re-check for the international departure)

For example if you are flying all DL, JFK is a much better option because the domestic and international operations are next to each other in T2/T4 where at ORD the international flights are all SkyTeam partners so leave out of T5 (while the DL flights go into T2). If you are flying United connecting to *A, ORD is the best option.

If flying in the night before, I agree that ORD is the much better option (I've lived in Chicago and my family lives in NYC so I have extensive experience with both). Hotels are plentiful near ORD and it's really easy to hop on the blue line and go into the city for a nice meal and walk around.