I think that the only 777 model that the 787 will compete directly against is the A market version. A market sales though have been relatively low ever since the ER
came around. The 787 long range version will seat far fewer people than the 772. The 787 short range version will have relatively similar capacity compared to a 772, but will not have the range. It will compete with the short range 777 versions, but these sales are already limited, so I don't think Boeing is comprosing 777 program.
Remember that quotes from manufacturers are usually a large over estimate of the seats in an airplane compared to the actual configuration. Correct me if I am wrong, but Boeing calculations for capacity call for a 60 inch pitch first class and a 40 inch pitch business class. Those are far less then what most airlines actually put in a plane. I would take the 250 seat figure with a grain of salt, because correct me if am wrong, but no airline has announced how many seats they will actually put in the 787.
It is true that the 787 and 777 compete, but they should complement each other. Many people thought that the 777 would canibalize 767 sales because Boeing didn't have room for another widebody twin. But in reality the 777 has proved to be a success, and the 767 sales didn't die off immediately. 767 sales have dimished recently because it is an old design that isn't competetive and the new Airbus offerings are better and Boeing has committed to the 787 which is a 767 replacement.
I think both will succeed, but the 777 is a ten year old design so the base versions are getting outdated. Future growth will be with the newer 772ER, LR
and 773ER, but the plane will need a more comprehensive update in the coming years; most likely to occur after a 737 replacement is done.
If you have never designed an airplane part before, let the real designers do the work!