Weight for weight, a 777-200 is more economic to run than a 747-400. However, capacity is reduced slightly in the 777-200. BA has found this out and the 772 has taken some 744 routes to save money. A more modern engine on the 744 would, no doubt, reduce the 772's advantage.
The slight reduction in capacity of the 772 is then more than made up for by using the 744 on routes with high premium-seat demand.