Both lie-flat business class products are about the same.
The United 777 from IAD-LHR is sometimes swapped out for a slightly different kind of United 777 which has the "old international business class" product, which has reclining seats that are more like Barcaloungers and does not have the nice new lie-flat beds. This can be a problem on an eastbound overnight flight (when sleep is a big deal) and is less of a problem on westbound flights if you're planning to stay awake during the whole flight. This equipment change can happen at any time, even hours before departure, until the entire United 777 fleet is completely reconfigured with the new business-class product (which should be happening soon -- not many old 777s left). In the rare event that a 777 swap does happen, SOP is to give you a $350 voucher to say "sorry about that".
Only real difference in the C class is that the 767 is 2-2-2 seating and 777 is 2-4-2.
The 777 BF cabin is split into two, with two rows forward of the galley, making a fairly secluded section whilst the 767 is one cabin with five rows of seats. Both aircraft have forward and backward facing seating.
If you are flying overnight eastbound, 767 centre aisle is guaranteed that you won't be disturbed, and can move about freely. In both aircraft, if you are in the window seat or middle seats getting out when your neighbour has the seat fully flat is difficult without disturbing them.