Having flown both myself, I'll have to agree with everyone above with two exceptions:

1) If the food is important to you, and you want Western cuisine I think the AA product is better.
2) I think that the AA Flagship F is more comfortable than the old JL Solo. I haven't kept up with the new JL suites (although I'm sure they're more comfortable than AA), but I don't know if they have switched over all of the planes they use on their transpac routes.