I've been through both and found the AA lounge to be very empty (we were the only 2 passengers for about an hour), relatively bright but quite sterile feeling, and with mediocre catering.

In contrast we found LATAM to be large, busier but with a lot of seating areas varying from sleeping areas to dining to sitting relatively alone, to a large group board table etc. I thought the catering there was much better and my only criticisms were the relative lack of apron view (albeit AA didn't have any view if I recall correctly) and there weren't huge numbers of plug points to charge gadgets.

YMMV obviously but I'd go back to LATAM in future and probably skip AA!