To my knowledge there's only a single daily AA flight with an F cabin between JFK and LHR --- if that timing doesn't suit, your choice is quite easy.

That said, there are a few interesting benefits of AA F that may (or may not) be of interest:

the LHR T3 CX First lounge has delightful food and drink offerings --- more limited, but imo higher quality, than the CCR

the newly opened JFK pre-dining facility for AA F passengers has received some high praise (I haven't tried it)

The AA 777W cabin has only 8 seats, but 2 dedicated washrooms --- ime, there's never a wait.