When doing the research, it is important to break down what is a government tax (fee) and what is a carrier surcharge. There are no longer any fuel surcharges across the North Atlantic.
The former are not only higher xEU, but distinctly higher xUK due to the APD. Those are all fixed and are the same no matter what carrier (although the APD is higher for premium cabins). Nothing to be done about it.
Surcharges are another thing and that is why it is important to break them out. You won't pay them for LON-NYC on DL, AA, or UA. But, you will most definitely pay them for BA & VS.
Bottom line is to look at the total outlay in miles/points and cash and make a decision as to what is important to you in terms of cost, convenience and product. Departure and arrival airport might matter as well depending on where you originate and terminate in the NYC and LON areas.