Someone with better access to seat maps than I could probably confirm this, but as of now, AA's JV partners BA/IB/AY will have slightly more daily seats out of JFK in peak S18 (I picked a random day in July to check) than AA will. About 2730 vs 2800 by my count. Probably the first time this has happened since the announcement of the JV.

Some fuel for the "what's AA doing with JFK" fire: at least 75% of those total TATL JV seats go to the JV hubs LHR, MAD, and HEL with only 6 flights/day to actual spokes. If EI gets added to the JV, over 80% of seats will be to JV hubs and only 5 flights/day to spokes.