Personally, I prefer the 777 over the 744 for comfort and ambience, particularly because it's much quieter, even behind the wing if you get stuck that far back, and because of the overhead design which gives such a feeling of space.
The 3-3-3 BA configuration means that as a singleton you get the same basic advantages and disadvantages of layout on both aircraft, unlike a 2-5-2 on a 777, which raises markedly different issues from those raised by a 3-4-3.
Of course, the 777 is supposed to be a higher yield aircraft, which theoretically ought to tend to mean that the cheap seats sell out quicker ...