There's one big advantage with BA: in the evening there are numerous flights from JFK to LHR, sometimes every half hour. More than once I changed my flight (of course your booked ticket has to allow free changes). Can be very useful when you are connecting from an other flight...

Without BA emerald status you probably don't have too many advantages choosing BA: first class check-in in NY with direct TSA security, seat selection and first class lounge access in NY and LHR are restricted to One World emeralds. The Swiss and the BA Business lounges in NY are similar, the BA one has an Elemis spa which could be useful. BA lounges in LHR are far superiour to the Swiss Business lounge in ZRH.