I went to New York last year and booked AA flight numbers as it was cheaper but flew on BA metal both ways.
As The_Banking_Scot states, you will received fewer Avios for the cabin bonus, as demonstrated by my two bookings last year, the second one shown below was using BA flight number:
NEW YORK-JOHN F KENNEDY - LONDON HEATHROW (C/J) AA6133
Tier points 140
Avios 3,452
Cabin Bonus 863
Tier Bonus 3,452
When I booked and flew on BA flight numbers and metal, I received:
NEW YORK-JOHN F KENNEDY - LONDON HEATHROW (J/R) BA172
Tier points 140
Avios 3,458
Cabin Bonus 1,729
Tier Bonus 3,458