I am in the fortunate position of flying both the 787 and 777.
The 787 burns around the same as a 757 yet is larger than a 767 and can do it ULR. Reliabilty is an issue but it is improving all the time as the aircraft settles down. It will be a while before it reaches the truly outstanding levels of the 777 but its a fine aircraft that you most certainly feel healthier in after a long flight.
It handles like a little go-cart compared to the 777 and features like cruise flaps are truly innovative from a cost per mile basis. Electronic CB's etc are nice, not having a touch screen CDU is a pain and the overall data presentation possibilities seem rather excessive. All in all it will be a stellar performer with time but then any company that can produce the brilliant 777 should be given time. Just about everyone I know who fly both prefer to fly the 777 (from a handling/size point of view). A derated EFATO leaves almost no spare performance. It feels like its entire design from start to finish is optimised to reduce fuel burn. The 787 is the starting ground for the 777X although interestingly I understand the 777X will still retain bleed air for the Cabin.