The BA lounge is nice when it is quiet and has internet and better snacks such as sandwiches than the AA lounge
AA lounge in terminal D is good for an AA Admiral's club but internet access isnt free; if wanting to eat, the paid offerings in the AA lounge are better than the free options at BA but no food for free
As far as alcohol options go, not drinking I havent paid attention to current offerings in either lounge but last time I was there, the BA lounge did have perrier which AA didnt. Basic alcohol offerings are now free at the AA lounge iirc
Rather than rely on others reports, why not try the BA lounge and see what you think and if disappointed it's only a short distance to the AA one