Looking only at American flights. Using miles one way and buying the other. Don't want this to become an American Airline bashing tread either.
We fly through JFK all the time, generally without any issues but we aren't connecting and I'm assuming you're looking at your regular May time frame so weather shouldn't be a concern at JFK.
If it's a matter of a stop one way or the other, and depending on the time of year, I'd probably do Charlotte, but that said, I've never connected there. Two fairly common problems at JFK can be the lack of available landing gates and/or a problem with baggage handling taking forever. Oh yeah! And then there's US C & I but I've read that can also be a problem at Charlotte.