At least you have the choice! I'd go with BA 777 no question. Unless you plan to fly the 7E7 at First Choice, you should definitely take the opportunity to fly the 777 from what I hear. Plus, BA has a wide variety of routes on the 777 - although you would likely do primarily EWR, IAD and Saudi for the first few years...
You'd definitely get a lot more rest during the summer season flying for BA.... Don't give up this opportunity to be an elitest NIGEL....